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°