Question

In the figure, ∠4 is an exterior angle to AUL.

a) Explain why ∠4 is equal to the sum of the measures of the two nonadjacent interior angles.

b) What is m∠4?

*I'm not good at these types of problems, I have a hard time trying to figure out where to start*

Answer 1

∠3=103° so that means ∠4 must equal 77°

Answer 2

a) see explanation below.

b) measure of ∠4 = 77°.

Explanation:

Given a figure ∠4 is an exterior angle to ΔAUL.

a) We have to explain why ∠4 is equal to the sum of the measures of the two nonadjacent interior angles.

That is why ∠4 = ∠1 +∠2

Lets first ∠1 +∠2 = 52° +25° = 77°

angle sum property of triangle states that the sum of angles of a triangle is always equal to 180°.

Thus, ∠1 +∠2 + ∠3 = 180°

Substitute the know value and find the angle 3.

⇒ 77° + ∠3 = 180°

⇒ ∠3 = 180° - 77° = 103°

Also ∠3 + ∠4 = 180° (Linear pair )

⇒ ∠4 = 180° - 103° = 77°.

⇒ ∠4 = ∠1 +∠2

Thus, ∠4 is equal to the sum of the measures of the two nonadjacent interior angles.

b) Measure of ∠4 = 77°.