Question

If ray NP bisects <MNQ, m<MNQ=(8x+12)°, m<PNQ=78°, and m<RNM=(3y-9)°, find the value of x and y

Answer 1

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

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

Answer 2

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°