Question

Given that m\angle LOM = 57∘ and m\angle LON = 136∘, find the measure of ∠MON.

Answer 1

The measure of ∠MON is found by subtracting the sum of the measures of ∠LOM and ∠LON from 360°, which gives us 167°.

Step-by-step explanation:

To find the measure of ∠MON given that m∠LOM = 57° and m∠LON = 136°, we need to know that the sum of angles around a point is 360°.

Since ∠LOM and ∠LON are adjacent angles that together form a larger angle ∠MON, we can find the measure of ∠MON by subtracting the sum of the measures of ∠LOM and ∠LON from 360°.

Adding the given angles:

57° + 136° = 193°

Now, subtract this sum from 360° to find the measure of ∠MON:

360° - 193° = 167°

So, the measure of ∠MON is 167°.