Question

Can someone help me solve the answer please?

Answer 1

Linear Pair:

A linear pair of angles is formed when two lines intersect.

A linear pair of angles must add up to 180°.

Given:

angle MON = 8x - 13°

angle LOM = 7x - 17°

To Find:

The measure of angle MON .

Solution:

angle MON + angle LOM = 180°

or, (8x - 13°) + (7x - 17°) = 180°

or, 15x - 30°= 180°

or, 15x = 180° + 30°

or, x = 210/15 = 14°

Answer:

angle MON = 8x - 13°

By putting the value of x, we get

angle MON = 8(14) - 13°

angle MON = 99°

Answer 2

m∠MON = 99°

Explanation:

A "straight angle" has a measure of 180°, so the two given angles will have that value as their sum.

m∠MON +m∠LOM = m∠LON

(8x -13°) +(7x -17°) = 180°

15x -30° = 180° . . . . collect terms

x -2° = 12° . . . . . . . . divide by 15

x = 14° . . . . . . . . . . . add 2°

Now we can find the measures of the angles.

m∠MON = 8x -13° = 8(14°) -13°

m∠MON = 99°

_____

Check

m∠LOM = 7x -17° = 7(14°) -17° = 81°

The sum of 81° and 99° is 180°, as it should be.