Question

Plz Help

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


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

(b) What is m∠4 ?

Answer 1

The answer in the procedure

Explanation:

Part A)

we know that

The measures of interior angle in a triangle must be equal to 180 degrees

In the triangle AUL

`m>3+25\°+52\°=180\°`

`m>3=103\°`

`m<3+m<4=180\°` -----> by supplementary angles

`m<4=180\°-m<3`

`m<4=180\°-103\°=77\°`

The sum of the two nonadjacent interior angles is equal to

`25\°+52\°=77\°`

therefore

m<4 is equal to the two nonadjacent interior angles

Part B)
`m<4=77\°` ----> see the Part A)