HURRY PLEASE if ray NP bisects angle MNQ and measure of angle MNQ= 8x + 12 and measure of PNQ= 78 degrees and measure of angle RNM= 3y -9, find the values of x and y

the measure of x is 18° and the measure of y is 29°

Step-by-step explanation:

Step 1

Find the measure of angle x

we know that

If ray NP bisects <MNQ

then

m<MNQ=m<PNM+m<PNQ > equation A

and

m<PNM=m<PNQ > equation B

we have that

m<MNQ=(8x+12)°

m<PNQ=78°

so

substitute in equation A

(8x+12)=78+78> 8x+12=156> 8x=156-12

8x=144> x=18°

Step 2

Find the measure of angle y

we have

m<PNM=(3y-9)°

m<PNM=78°

so

3y-9=78> 3y=87> y=29°

therefore

the answer is

the measure of x is 18° and the measure of y is 29°

180-142=38 for the acute angle next to the entry

90+38=128

180-128=52

a=52

step-by-step explanation: