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tatuchka
2 months ago
8

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

Mathematics
1 answer:
AnnZ [12.3K]2 months ago
7 0

Step 1

Calculate angle x

Given:

If ray NP divides <MNQ evenly, then

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

and

m<PNM = m<PNQ -------> equation B

We know:

m<MNQ = (8x + 12)°

m<PNQ = 78°

Substitute into equation A:

(8x + 12) = 78 + 78 ------> 8x + 12 = 156 ------> 8x = 144

x = 18°

Step 2

Calculate angle y

We have:

m<PNM = (3y - 9)°

m<PNM = 78°

So,

3y - 9 = 78 ------> 3y = 87 ------> y = 29°

Thus,

The solution is

x is 18° and y is 29°


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