< 1 and < 2 are a linear pair m< 1=77+2x and m< 2=8x+23. find m< 1

A linear pair of angles are supplementary angles, which means they add up to 180 degrees.

This makes sense because a linear pair of angles form a straight line, which is 180 degrees.

Since m∠1 and m∠2 are a linear pair, make them add up to 180 in an equation. Your equation should look like this:

m∠1 + m∠2 = 180

Substitute in the measures of ∠1 and ∠2 into the equation. Now your equation should look like this:

(77 + 2x) + (8x + 23) = 180

Combine like terms (77 + 23) and (2x + 8x).

100 + 10x = 180

Subtract 100 from both sides.

10x = 80

Divide both sides by 10.

x = 8

Plug 8 for x in m∠1.

77 + 2(8) = 77 + 16

77 + 16 = 93

m∠1 = 93°