Question

In the figure below, the measure of ZLON is 152°. What is the measure, indegrees, of ZMON?4

Answer 1

Hello there. To solve this question, we have to remember some properties about angles.

Given the following diagram:

We know that:

`\angle LON=152^(\circ)`

And the image shows that

`\angle LOM=78^(\circ)`

We want to determine the measure of

`\angle MON`

That is, the following angle in blue:

For this, notice that

`\angle LOM+\angle MON=\angle LON`

Therefore we found an equation that can give us the answer.

Plugging the values, we have that

`78^(\circ)+\angle MON=152^(\circ)`

Subtract 78º on both sides of the equation.

`\angle MON=152^(\circ)-78^(\circ)=74^(\circ)`

This is the measure in degrees that we're looking for.