Question

if the measure of angle 2 is 3x and the measure of angle 1 is 5x-12 then what is the measure of angle 9?

Answer 1

The measure of angle 9 is 108°.

Explanation:

We are told that the measure of angles 3,4, 11, 12 are 67, 113, 67, 113 respectively, this means that the lines p and q are parallel.

Further, this means

angle 1 = angle 9 ,

angle 2 = angle 10.

We are also told that

`angle\: 2=3x`

`angle\:1=5x-12`

Since angles 1 and 2 are supplementary, they add up to 180°:

`\angle 1+\angle 2=180^o`

so we have

`3x+(5x-12)=180^o`

`8x-12=180^o`

`\boxed{x=24}`

With this value of x we find the numerical value of angle 1 :

`angle\:1=5x-12=5(24)-12=108^o\\\\\ angle\: 1=108^o`

since angle 1 = angle 9

`\boxed{angle\:9=108^o}`