Question

I need help please……………..

Answer 1

m∠L = 31°

m∠N = 66°

m∠M = 83°

Explanation:

• The Triangle Sum Theorem says that the sum of a triangle's interior angles equals 180°.

Finding x:

Thus, we can find x by setting the sum of the three angles equal to 180:

m∠L + m∠N + m∠M = 180

(x + 9) + (3x) + (4x - 5) = 180

(x + 3x + 4x) + (9 - 5) = 180

(8x + 4 = 180) - 4

(8x = 176) / 8

x = 22

Thus, x = 22.

Finding m∠L:

Now we can find m∠L by substituting 22 for x in (x + 9):

m∠L = 22 + 9

m∠L = 31

Thus, m∠L = 31°.

Finding m∠L:

Now we can find m∠N by substituting 22 for x in 3x:

m∠N = 3(22)

m∠N = 66

Thus, m∠N = 66°.

Finding m∠M:

Now we can find m∠M by substituing 22 for x in (4x - 5):

m∠M = 4(22) - 5

m∠M = 88 - 5

m∠M = 83

Thus, m∠M = 83°.

Check the validity of the answers:

We can check that our answers are correct by seeing whether the sum of the three angles equals 180:

31 + 66 + 83 = 180

97 + 83 = 180

180 = 180

Thus, our answers are correct.