Supplementary angles add up to 180°. Then if we add the measures of angles <1 and <2 we should get 180°, like this:
m<1 + m<2 = 180
By replacing 4x + 3 for m<1 and 3x - 5 for m<2 into the above equation, we get:
(4x + 3) + (3x - 5) = 180
4x + 3 + 3x - 5 = 180
4x + 3x + 3 - 5 = 180
7x - 2 = 180
7x = 180 + 2
7x = 182
x = 182/7 = 26
Then, x equals 26, the third option is the correct answer