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

Answer:

The measure of angle 9 is 108°.

Step-by-step 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

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