Solve for x. i need to know how to do this

A straight line is 180°. ∠LMP and ∠PMN make up the 180°. Or (-16x + 13)° and (-20x + 23)° add up to 180°, so:

(-16x + 13) + (-20x + 23) = 180°

-16x + 13 - 20x + 23 = 180  Combine like terms

-36x + 36 = 180  Subtract 36 on both sides

-36x = 144  Divide -36 on both sides

x = -4

x = -4

The two marked angles (∠LMP, ∠PMN) add to make a straight line. As a consequence, they are called linear angles. They are supplementary, meaning they add to give 180°.

To find x, add them up and find the value of x that makes the sum be 180°

... (-16x +13)° +(-20x +23)° = 180°

... -36x +36 = 180 . . . . . . collect terms, divide by °

... 1 - x = 5 . . . . . . . . . . . . divide by 36

... 1 - 5 = x = -4 . . . . . . . . . add x-5

Check

∠LMP = (-16x+13)° = (-16·(-4) +13)° = 77°

∠PMN = (-20x+23)° = (-20·(-4) +23)° = 103°

... 77° + 103° = 180° . . . . . the answer checks OK

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step-by-step explanation: