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°