Question

A right triangle has a exterior angle with a measure of 160 degrees. Can you determine the measure of the interior angles? Explain.

Answer 1

x = 70°

Explanation:

Well, the measurement of an exterior and the corresponding interior angle have to equal 180°. So that means the exterior angle, let's call it "e", plus the interior angle, let's call it "i", have to equal 180°:

e + i = 180°

Well, you know the measurement of the exterior angle, so we can solve for i to find the interior angle:

160° + i = 180°

i = 180° - 160°

i = 20°

Now, we know this is a right triangle, so that means one angle is equal to 90°. All of the angles must add to equal 180° in a triangle, so we can solve for "x" to find the unknown angle with this equation:

20° + 90° + x = 180°

110° + x = 180°

x = 180° - 110°

x = 70°

Answer 2

Well, the measurement of an exterior and the corresponding interior angle have to equal 180°. So that means the exterior angle, let's call it "e", plus the interior angle, let's call it "i", have to equal 180°:

e + i = 180°

Well, you know the measurement of the exterior angle, so we can solve for i to find the interior angle:

160° + i = 180°

i = 180° - 160°

i = 20°

Now, we know this is a right triangle, so that means one angle is equal to 90°. All of the angles must add to equal 180° in a triangle, so we can solve for "x" to find the unknown angle with this equation:

20° + 90° + x = 180°

110° + x = 180°

x = 180° - 110°

x = 70°