# Basic Geometry : How to find an angle in a right triangle

## Example Questions

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### Example Question #1 : How To Find An Angle In A Right Triangle

Find angle C.

C=72

None of these

C=53

C=70

C=65

C=65

Explanation:

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:

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

Simplify and solve for C.

### Example Question #1 : How To Find An Angle In A Right Triangle

Which of the following can be two angle measures of a right triangle?

Explanation:

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:

The remaining choice is correct:

### Example Question #1 : How To Find An Angle In A Right Triangle

A right triangle has an angle that is 15 more than twice the other.  What is the smaller angle?

Explanation:

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 =  first angle and = second angle

So the equation to solve becomes or

Thus, the first angle is and the second angle is .

So the smaller angle is

### Example Question #1 : How To Find An Angle In A Right Triangle

Angle  in the triangle shown below (not to scale) is 35 degrees. What is angle ?

degrees

degrees

degrees

degrees

degrees

Explanation:

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

Angle  is equal to 55 degrees.

### Example Question #1 : How To Find An Angle In A Right Triangle

Which of the following cannot be true of a right triangle?

One leg can be longer than the hypotenuse.

A right triangle can have an obtuse angle.

A right triangle can be equilateral.

None of the other statements can be true of a right triangle.

The measures of the angles of a right triangle can total .

None of the other statements can be true of a right triangle.

Explanation:

All of these statements are false.

A right triangle can be equilateral.

False: An equilateral triangle must have three angles that measure  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 .

False: The measures of any triangle total .

### Example Question #1 : How To Find An Angle In A Right Triangle

In triangle , what is the measure of angle ?

Explanation:

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

To solve for the measure of angle , we plug in the values of and . Since angle is a right angle, we know the measure will be .

### Example Question #1 : How To Find An Angle In A Right Triangle

Find the degree measure of the missing angle.

Explanation:

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

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

Therefore, the third angle measures 43º.

### Example Question #1 : How To Find An Angle In A Right Triangle

The right triangle  has two equal angles, what is each of their measures?

Explanation:

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.

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

### Example Question #2 : How To Find An Angle In A Right Triangle

What is the missing angle in this right triangle?

Explanation:

The angles of a triangle all add up to .

This means that .

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

.

Solve for :