Question

If ON is congruent to OL, find m OML

Answer 1

Answer:
measure angle OML = 26°

Explanation:
Let's consider the two triangles OML and OMN, we have:
measure angle MOL = measure angle MON
ON = OL
OM is a common sides

Therefore, based on SAS (side-angle-side):
ΔOML is congruent to ΔOMN

From this congruency, we have:
measure angle L = measure angle N
9x - 8 = 7x + 8
9x - 7x = 8 + 8
2x = 16
x = 8

Therefore:
measure angle L = 9(8) - 8 = 64°
measure angle N = 7(8) + 8 = 64°

Now, in triangle OML, we have:
angle NOM is an exterior angle of the triangle. This means that its measure is equal to the summation of the other two non-adjacent angles.
This means that:
measure angle NOM = measure angle L + measure angle OML
90 = 64 + measure angle OML
measure angle OML = 90 - 64 = 26°

Hope this helps :)