Answer:
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.