First, know that all the angles in a triangle add up to 180 degrees.

Each triangle has 3 angles.  Thus, we have the sum of three angles as shown:

 \(\displaystyle 180=A+B+C\)

where we have angles A, B, and C. In our right triangle, one angle is 25 degree and we'll call that angle A. The other known angle is 90 degrees and we'll call this angle B.  Thus, we have

\(\displaystyle 180=25+90+C\)

Simplify and solve for C.

\(\displaystyle 180=115+C\)

\(\displaystyle C=65\)

A right triangle cannot have an obtuse angle; this eliminates the choice of 100 and 10.

The acute angles of a right triangle must total 90 degrees. Three choices can be eliminated by this criterion:

\(\displaystyle 60+40=100\)

\(\displaystyle 38+42=80\)

\(\displaystyle 60+60=120\)

The remaining choice is correct: \(\displaystyle 35+55=90\)

The sum of the angles in a triangle is 180.  A right triangle has one angle of 90.  Thus, the sum of the other two angles will be 90.

Let \(\displaystyle x\) =  first angle and \(\displaystyle 2x + 15\) = second angle

So the equation to solve becomes \(\displaystyle x+ 2x+15 = 90\) or \(\displaystyle 3x=75\)

Thus, the first angle is \(\displaystyle 25\) and the second angle is \(\displaystyle 65\).

So the smaller angle is \(\displaystyle 25\)

The interior angles of a triangle always add up to 180 degrees. We are given angle \(\displaystyle A\) and since this is indicated to be a right triangle we know angle \(\displaystyle C\) is equal to 90 degrees. Thus we know 2 of the 3 and can determine the third angle.

\(\displaystyle 180-35-90=55\)

Angle \(\displaystyle B\) is equal to 55 degrees.

All of these statements are false.

A right triangle can be equilateral.

False: An equilateral triangle must have three angles that measure \(\displaystyle 60^{\circ }\) each.

One leg can be longer than the hypotenuse.

False: Each leg is shorter than the hypotenuse.

A right triangle can have an obtuse angle.

False: Both angles of a right triangle that are not right must be acute.

The measures of the angles of a right triangle can total \(\displaystyle 160^{\circ }\).

False: The measures of any triangle total \(\displaystyle 180^{\circ }\).

The formula to find all the angles of a triangle is:

\(\displaystyle \measuredangle A\)\(\displaystyle +\) \(\displaystyle \measuredangle B\)\(\displaystyle +\) \(\displaystyle \measuredangle C\)\(\displaystyle =\)\(\displaystyle 180^{\circ}\)

To solve for the measure of angle \(\displaystyle C\), we plug in the values of \(\displaystyle A\) and \(\displaystyle B\). Since angle \(\displaystyle A\) is a right angle, we know the measure will be \(\displaystyle 90^{\circ}\).

\(\displaystyle 90^{\circ}\)\(\displaystyle +\)\(\displaystyle 35^{\circ}\)\(\displaystyle +\) \(\displaystyle \measuredangle C\)\(\displaystyle =\)  \(\displaystyle 180^{\circ}\)

\(\displaystyle \measuredangle C\)\(\displaystyle =\)\(\displaystyle 55^{\circ}\)

All the angles in a triangle add up to 180º.

To find the value of the remaining angle, subtract the known angles from 180º:

 \(\displaystyle 180º- 90º- 47º= 43º\)

Therefore, the third angle measures 43º.

The internal angles of a triangle always add up to 180 degrees, and it was given that the triangle was right, meaning that one of the angles measures 90 degrees.

This leaves 90 degrees to split evenly between the two remaining angles as was shown in the question.

\(\displaystyle 180-90=90\)

\(\displaystyle \frac{90}{2}=45\)

Therefore, each of the two equal angles has a measure of 45 degrees.

The angles of a triangle all add up to \(\displaystyle \small 180^o\).

This means that \(\displaystyle \small x + 34 + 90 = 180\).

Using the fact that 90 is half of 180, we can figure out that the missing angle, x, plus 34 adds to the remaining 90, and we can just subtract

\(\displaystyle \small 90 - 34 = 56\).

The angles of a triangle add together to 180 degrees. We already know that one of the angles is 90 degrees, so we can subtract 90 from 180: the other 2 angles have to add to 90 degrees.

We can now subtract to get x:

\(\displaystyle \small 90 - 49 = 41\)