How to find an angle in an acute / obtuse isosceles triangle - Math
Card 0 of 124
An isoceles triangle has a vertex angle that is twenty more than twice the base angle. What is the difference between the vertex and base angles?
An isoceles triangle has a vertex angle that is twenty more than twice the base angle. What is the difference between the vertex and base angles?
A triangle has 
degrees. An isoceles triangle has one vertex angle and two congruent base angles.
Let 
= the base angle and 
= vertex angle
So the equation to solve becomes 
or
so the base angle is 
and the vertex angle is 
and the difference is 
.
A triangle has
Let
So the equation to solve becomes
or
so the base angle is
Compare your answer with the correct one above
An ssosceles triangle has interior angles of 
degrees and 
degrees. Find the missing angle.
An ssosceles triangle has interior angles of
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 
degrees.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
Compare your answer with the correct one above
The largest angle in an obtuse isosceles triangle is 
degrees. Find the measurement of one of the two equivalent interior angles.
The largest angle in an obtuse isosceles triangle is
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 
degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
Compare your answer with the correct one above
The two equivalent interior angles of an obtuse isosceles triangle each have a measurement of 
degrees. Find the measurement of the obtuse angle.
The two equivalent interior angles of an obtuse isosceles triangle each have a measurement of
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 
degrees.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
Compare your answer with the correct one above
In an obtuse isosceles triangle the angle measurements are, 
, 
, and 
. Find the measurement of one of the acute angles.
In an obtuse isosceles triangle the angle measurements are,
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
The solution is:
However, 
degrees is the measurement of both of the acute angles combined.
Each individual angle is 
.
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
However,
Each individual angle is
Compare your answer with the correct one above
In an acute isosceles triangle the two equivalent interior angles each have a measurement of 
degrees. Find the missing angle.
In an acute isosceles triangle the two equivalent interior angles each have a measurement of
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
Compare your answer with the correct one above
In an acute isosceles triangle the two equivalent interior angles are each 
degrees. Find the missing angle.
In an acute isosceles triangle the two equivalent interior angles are each
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
Compare your answer with the correct one above
The largest angle in an obtuse isosceles triangle is 
degrees. Find the measurement of one of the equivalent interior angles.
The largest angle in an obtuse isosceles triangle is
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse Isosceles triangle, the two missing angles must be acute angles.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
Compare your answer with the correct one above
In an obtuse isosceles triangle the largest angle is 
degrees. Find the measurement of one of the acute angles.
In an obtuse isosceles triangle the largest angle is
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
Compare your answer with the correct one above
In an acute isosceles triangle the measurement of the non-equivalent interior angle is 
degrees. Find the measurement of one of the equivalent interior angles.
In an acute isosceles triangle the measurement of the non-equivalent interior angle is
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
Compare your answer with the correct one above
In an obtuse isosceles triangle, the largest interior angle is 
degrees. What is the measurement of one of the equivalent interior angles?
In an obtuse isosceles triangle, the largest interior angle is
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
Compare your answer with the correct one above
You are flying a kite at an altitude of 40 feet after having let out 75 feet of string. What is the kite's angle of elevation from where you are holding the spool of string at a height of 4 feet off the ground? Round answer to one decimal place.
You are flying a kite at an altitude of 40 feet after having let out 75 feet of string. What is the kite's angle of elevation from where you are holding the spool of string at a height of 4 feet off the ground? Round answer to one decimal place.
First, we must draw a picture to include all important parts given in the problem.
Once this is determined we can use trigonometry to find the angle of elevation.
Use the inverse sin on a calculator to solve.
First, we must draw a picture to include all important parts given in the problem.
Once this is determined we can use trigonometry to find the angle of elevation.
Use the inverse sin on a calculator to solve.
Compare your answer with the correct one above
Two angles in an isosceles triangle are 50 and 80 degrees respectively. What is the measure of the third angle?
Two angles in an isosceles triangle are 50 and 80 degrees respectively. What is the measure of the third angle?
If a triangle is isosceles, two of the angles must be congruent. So the angle must be either 50 degrees or 80 degrees.
We know that the three angles in all triangles must sum to equal 180 degrees. The only answer choice that is both the same as one of the given angles and results in a sum equal to 180 degrees is the 50 degree angle.
50+50+80=180.
If a triangle is isosceles, two of the angles must be congruent. So the angle must be either 50 degrees or 80 degrees.
We know that the three angles in all triangles must sum to equal 180 degrees. The only answer choice that is both the same as one of the given angles and results in a sum equal to 180 degrees is the 50 degree angle.
50+50+80=180.
Compare your answer with the correct one above
An isosceles triangle has one angle measuring 
. Which of the following are possible values for angles in this triangle?
An isosceles triangle has one angle measuring
An isosceles triangle has 2 congruent angles and then a third angle. These angles, as in any triangle, must add to 180.
One possibility is that the 25-degree angle is the "different" one, and the other two are congruent. This could be expressed using the algebraic expression 
. To find the other two angles, solve for x. First combine like terms:
subtract 25 from both sides
divide both sides by 2
The other possibility is that there are 2 25-degree angles and then some different angle measure. This could be expressed using the algebraic expression 
. Again, solve for x. First add the 2 25's to get 50:
subtract 50 from both sides
An isosceles triangle has 2 congruent angles and then a third angle. These angles, as in any triangle, must add to 180.
One possibility is that the 25-degree angle is the "different" one, and the other two are congruent. This could be expressed using the algebraic expression
The other possibility is that there are 2 25-degree angles and then some different angle measure. This could be expressed using the algebraic expression
Compare your answer with the correct one above
Refer to the above triangle. By what statement does it follow that 
?
Refer to the above triangle. By what statement does it follow that
We are given that, in 
, two sides are congruent; specifically, 
. It is a consequence of the Isosceles Triangle Theorem that the angles opposite the sides are also congruent - that is, 
.
We are given that, in
Compare your answer with the correct one above
Points A and B lie on a circle centered at Z, where central angle <AZB measures 140°. What is the measure of angle <ZAB?
Points A and B lie on a circle centered at Z, where central angle <AZB measures 140°. What is the measure of angle <ZAB?
Because line segments ZA and ZB are radii of the circle, they must have the same length. That makes triangle ABZ an isosceles triangle, with <ZAB and <ZBA having the same measure. Because the three angles of a triangle must sum to 180°, you can express this in the equation:
140 + 2x = 180 --> 2x = 40 --> x = 20
Because line segments ZA and ZB are radii of the circle, they must have the same length. That makes triangle ABZ an isosceles triangle, with <ZAB and <ZBA having the same measure. Because the three angles of a triangle must sum to 180°, you can express this in the equation:
140 + 2x = 180 --> 2x = 40 --> x = 20
Compare your answer with the correct one above
In triangle ABC, Angle A = x degrees, Angle B = 2x degrees, and Angle C = 3x+30 degrees. How many degrees is Angle B?
In triangle ABC, Angle A = x degrees, Angle B = 2x degrees, and Angle C = 3x+30 degrees. How many degrees is Angle B?
Because the interior angles of a triangle add up to 180°, we can create an equation using the variables given in the problem: x+2x+(3x+30)=180. This simplifies to 6X+30=180. When we subtract 30 from both sides, we get 6x=150. Then, when we divide both sides by 6, we get x=25. Because Angle B=2x degrees, we multiply 25 times 2. Thus, Angle B is equal to 50°. If you got an answer of 25, you may have forgotten to multiply by 2. If you got 105, you may have found Angle C instead of Angle B.
Because the interior angles of a triangle add up to 180°, we can create an equation using the variables given in the problem: x+2x+(3x+30)=180. This simplifies to 6X+30=180. When we subtract 30 from both sides, we get 6x=150. Then, when we divide both sides by 6, we get x=25. Because Angle B=2x degrees, we multiply 25 times 2. Thus, Angle B is equal to 50°. If you got an answer of 25, you may have forgotten to multiply by 2. If you got 105, you may have found Angle C instead of Angle B.
Compare your answer with the correct one above
Triangle FGH has equal lengths for FG and GH; what is the measure of ∠F, if ∠G measures 40 degrees?
Triangle FGH has equal lengths for FG and GH; what is the measure of ∠F, if ∠G measures 40 degrees?
It's good to draw a diagram for this; we know that it's an isosceles triangle; remember that the angles of a triangle total 180 degrees.
Angle G for this triangle is the one angle that doesn't correspond to an equal side of the isosceles triangle (opposite side to the angle), so that means ∠F = ∠H, and that ∠F + ∠H + 40 = 180,
By substitution we find that ∠F * 2 = 140 and angle F = 70 degrees.
It's good to draw a diagram for this; we know that it's an isosceles triangle; remember that the angles of a triangle total 180 degrees.
Angle G for this triangle is the one angle that doesn't correspond to an equal side of the isosceles triangle (opposite side to the angle), so that means ∠F = ∠H, and that ∠F + ∠H + 40 = 180,
By substitution we find that ∠F * 2 = 140 and angle F = 70 degrees.
Compare your answer with the correct one above
Sides 
and 
in this triangle are equal. What is the measure of 
?
Sides
This triangle has an angle of 
. We also know it has another angle of 
at 
because the two sides are equal. Adding those two angles together gives us 
total. Since a triangle has 
total, we subtract 130 from 180 and get 50.
This triangle has an angle of
Compare your answer with the correct one above
The vertex angle of an isosceles triangle is 
. What is the base angle?
The vertex angle of an isosceles triangle is
An isosceles triangle has two congruent base angles and one vertex angle. Each triangle contains 
. Let 
= base angle, so the equation becomes 
. Solving for 
gives 
An isosceles triangle has two congruent base angles and one vertex angle. Each triangle contains
Compare your answer with the correct one above