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°
Answer: If NP bisects MNQ, MNQ=8x+12,PNQ=78, and RNM=3y-9, find the values of x and y
x= 18 y=11
Step-by-step explanation:
We know that MNQ= 8x+12
PNQ=78 and MNP is equal to PNQ
Therefore, PNQ=MNP
So since these two angles make up MNQ,
Add 78+78 which is 156
So now we need to find x
The equation to find x is 8x+12=156
8x+12=156
8x=144
x=18
Now that we know x it is time to find y.
So we know that RNM=3y-9
And we know that MNQ is equal to 156
RNM an MNQ form a straight line which means that it is equal to 180 degrees
So the equation to find y is 3y-9+156=180
3y-9+156=180
3y+147=180
3y=33
y=11
So in conclusion, x=18 and y=11
Hope this helped! :3
