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Intermediate Geometry : How to find an angle in an acute / obtuse isosceles triangle

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Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

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?

Possible Answers:

$\displaystyle 20$

$\displaystyle 60$

100 $\displaystyle 100$

$\displaystyle 40$

150 $\displaystyle 150$

Correct answer:

$\displaystyle 60$

Explanation:

A triangle has 180 $\displaystyle 180$ degrees. An isoceles triangle has one vertex angle and two congruent base angles.

Let $\displaystyle x$ = the base angle and $2x\ +\ 20$ $\displaystyle 2x\ +\ 20$ = vertex angle

So the equation to solve becomes $x\ +\ x\ +\ 2x\ +\ 20 = 180$ $\displaystyle x\ +\ x\ +\ 2x\ +\ 20 = 180$

$4x\ +\ 20=180$ $\displaystyle 4x\ +\ 20=180$

so the base angle is $\displaystyle 40$ and the vertex angle is 100 $\displaystyle 100$ and the difference is $\displaystyle 60$.

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Example Question #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

An ssosceles triangle has interior angles of $\displaystyle 32$ degrees and $\displaystyle 74$ degrees. Find the missing angle.

Possible Answers:

$37^\circ$ $\displaystyle 37^\circ$

$90^\circ$ $\displaystyle 90^\circ$

$74^\circ$ $\displaystyle 74^\circ$

$15^\circ$ $\displaystyle 15^\circ$

$32^\circ$ $\displaystyle 32^\circ$

Correct answer:

$74^\circ$ $\displaystyle 74^\circ$

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 180 $\displaystyle 180$ degrees.

Thus, the solution is:

$\displaystyle 32+74=106$

$\displaystyle 180-106=74$

$\displaystyle Check: 74+74+32=180$

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Example Question #2 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

The largest angle in an obtuse isosceles triangle is $\displaystyle 98$ degrees. Find the measurement of one of the two equivalent interior angles.

Possible Answers:

$42^\circ$ $\displaystyle 42^\circ$

$41^\circ$ $\displaystyle 41^\circ$

$82^\circ$ $\displaystyle 82^\circ$

$2^\circ$ $\displaystyle 2^\circ$

$90^\circ$ $\displaystyle 90^\circ$

Correct answer:

$41^\circ$ $\displaystyle 41^\circ$

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 180 $\displaystyle 180$ degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.

Thus, the solution is:

$\displaystyle 180-98=82$

$82\div2=41$ $\displaystyle 82\div2=41$

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Example Question #3 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

The two equivalent interior angles of an obtuse isosceles triangle each have a measurement of $\displaystyle 28$ degrees. Find the measurement of the obtuse angle.

Possible Answers:

$99^\circ$ $\displaystyle 99^\circ$

$112^\circ$ $\displaystyle 112^\circ$

$124^\circ$ $\displaystyle 124^\circ$

$56^\circ$ $\displaystyle 56^\circ$

$134^\circ$ $\displaystyle 134^\circ$

Correct answer:

$124^\circ$ $\displaystyle 124^\circ$

Explanation:

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Example Question #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

In an obtuse isosceles triangle the angle measurements are, $x^\circ$ $\displaystyle x^\circ$, $x^\circ$ $\displaystyle x^\circ$, and $(10x-2)=128^\circ$ $\displaystyle (10x-2)=128^\circ$. Find the measurement of one of the acute angles.

Possible Answers:

$4^\circ$ $\displaystyle 4^\circ$

$26^\circ$ $\displaystyle 26^\circ$

$13^\circ$ $\displaystyle 13^\circ$

$10^\circ$ $\displaystyle 10^\circ$

$32^\circ$ $\displaystyle 32^\circ$

Correct answer:

$13^\circ$ $\displaystyle 13^\circ$

Explanation:

The solution is:

$\displaystyle 180-154=26$

However, $\displaystyle 26$ degrees is the measurement of both of the acute angles combined.

Each individual angle is $26\div2=13$ $\displaystyle 26\div2=13$.

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Example Question #5 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

In an acute isosceles triangle the two equivalent interior angles each have a measurement of $\displaystyle 53$ degrees. Find the missing angle.

Possible Answers:

$53^\circ$ $\displaystyle 53^\circ$

$75^\circ$ $\displaystyle 75^\circ$

$62^\circ$ $\displaystyle 62^\circ$

$42^\circ$ $\displaystyle 42^\circ$

$74^\circ$ $\displaystyle 74^\circ$

Correct answer:

$74^\circ$ $\displaystyle 74^\circ$

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 180 $\displaystyle 180$ degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.

The solution is:

$\displaystyle 53+53=106$

$\displaystyle 180-106=74$

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Example Question #6 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

In an acute isosceles triangle the two equivalent interior angles are each $\displaystyle 55$ degrees. Find the missing angle.

Possible Answers:

$78^\circ$ $\displaystyle 78^\circ$

$13^\circ$ $\displaystyle 13^\circ$

$70^\circ$ $\displaystyle 70^\circ$

$62^\circ$ $\displaystyle 62^\circ$

$140^\circ$ $\displaystyle 140^\circ$

Correct answer:

$70^\circ$ $\displaystyle 70^\circ$

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 180 $\displaystyle 180$ degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.

The solution is:

$\displaystyle 55+55=110$

$\displaystyle 180-110=70$

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Example Question #7 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

The largest angle in an obtuse isosceles triangle is 138 $\displaystyle 138$ degrees. Find the measurement of one of the equivalent interior angles.

Possible Answers:

$23^\circ$ $\displaystyle 23^\circ$

$44^\circ$ $\displaystyle 44^\circ$

$15^\circ$ $\displaystyle 15^\circ$

$21^\circ$ $\displaystyle 21^\circ$

$42^\circ$ $\displaystyle 42^\circ$

Correct answer:

$21^\circ$ $\displaystyle 21^\circ$

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 180 $\displaystyle 180$ degrees. Since this is an obtuse Isosceles triangle, the two missing angles must be acute angles.

Thus, the solution is:

$\displaystyle 180-138=42$

$42\div2=21$ $\displaystyle 42\div2=21$

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Example Question #41 : Acute / Obtuse Isosceles Triangles

In an obtuse isosceles triangle the largest angle is 118 $\displaystyle 118$ degrees. Find the measurement of one of the acute angles.

Possible Answers:

$15^\circ$ $\displaystyle 15^\circ$

$62^\circ$ $\displaystyle 62^\circ$

$31^\circ$ $\displaystyle 31^\circ$

$18^\circ$ $\displaystyle 18^\circ$

$64^\circ$ $\displaystyle 64^\circ$

Correct answer:

$31^\circ$ $\displaystyle 31^\circ$

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 180 $\displaystyle 180$ degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.

The solution is:

$\displaystyle 180-118=62$

$62\div2=31$ $\displaystyle 62\div2=31$

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Example Question #41 : Acute / Obtuse Isosceles Triangles

In an acute isosceles triangle the measurement of the non-equivalent interior angle is $\displaystyle 86$ degrees. Find the measurement of one of the equivalent interior angles.

Possible Answers:

$52^\circ$ $\displaystyle 52^\circ$

$94^\circ$ $\displaystyle 94^\circ$

$45^\circ$ $\displaystyle 45^\circ$

$14^\circ$ $\displaystyle 14^\circ$

$47^\circ$ $\displaystyle 47^\circ$

Correct answer:

$47^\circ$ $\displaystyle 47^\circ$

Explanation:

Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 180 $\displaystyle 180$ degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.

The solution is:

$\displaystyle 180-86=94$

$94\div2=47$ $\displaystyle 94\div2=47$

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Intermediate Geometry : How to find an angle in an acute / obtuse isosceles triangle

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Example Question #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Example Question #2 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Example Question #3 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Example Question #1 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Example Question #5 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Example Question #6 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Example Question #7 : How To Find An Angle In An Acute / Obtuse Isosceles Triangle

Example Question #41 : Acute / Obtuse Isosceles Triangles

Example Question #41 : Acute / Obtuse Isosceles Triangles

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