MATH SOLVE

4 months ago

Q:
# If ON is congruent to OL, find m OML

Accepted Solution

A:

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 :)

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 :)