Question

In parallel lines cut by a transversal if m angle RNP =(8x+63) degree and m angle NRS = 5x degree

1. find angle measure of m angle RNP
2. Find angle measure of m angle NRS

Answer 1

Part 1)
`m\angle RNP=135^o`

Part 2)
`m\angle NRS=45^o`

Explanation:

The complete question in the attached figure

step 1

Find the value of x

we know that

`m\angle RNP+m\angle NRS=180^o` ----> by supplementary angles (consecutive interior angles)

substitute the given values

`(8x+63)^o+5x^o=180^o`

Solve for x

`8x+5x=180-63\\13x=117\\x=9`

step 2

Find the measure of angle RNP

substitute the value of x

`m\angle RNP=(8(9)+63)=135^o`

step 5

Find the measure of angle NRS

substitute the value of x

`m\angle NRS=5(9)=45^o`