Question

An exterior angle of a triangle is 124°. If the non-adjacent angles are congruent, then what are the measures of all of the interior angles of the triangle?

a.) 56°, 62°, 62°
b.) 124°, 28°, 28°
c.) 34°, 73°, 73°
d.) 90°, 45°, 45°

Answer 1

56, 62, 62.

Explanation:

By the external angle of a triangle theorem

m < A = m < B + m < C where A is the external angle and B and C are the 2 non-adjacent angles.

As m < B = m < C then

m < A = 2 *m < B

If the other internal angle is D then

m < B + m < C + m < D = 180 degrees

m < A = 124 degrees, so

124 + D = 180

D = 180 - 124 = 56 degrees.

So m < B ( and m < C) = 124 / 2 = 62 degrees.

Answer 2

Answer: Choice A) 56, 62, 62

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Work Shown:

Let x be the measure of each non-adjacent interior angle.

By the remote interior angle theorem, the two angles mentioned add up to the exterior angle 124

x+x = 124

2x = 124

2x/2 = 124/2

x = 62

So we have two interior angles of 62 degrees each. The third interior angle is 180-124 = 56 degrees. You can also find this by solving x+x+y = 180 for y.

A diagram is provided below.