Answer:
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°
