You have the following algebraic expression for the measures of angles
∠A and ∠B:
m∠A = (7x + 24)°
m∠B = (7x - 26)°
In order to find the measure of angle ∠A, you first consider that these angles, ∠A and ∠B are supplementary. This means that they add up 180°, that is, the sum of these angles form a straight angle. Thus, you have:
m∠A + m∠B = 180
(7x + 24) + (7x - 26) = 180
you solve ther previoues equation as follow:
(7x + 24) + (7x - 26) = 180 eliminate parenthesis
7x + 24 + 7x - 26 = 180 simplify similar terms
7x + 7x + 24 - 26 = 180
14x - 2 = 180 add 2 both sides
14x = 180 + 2
14x = 182 divide by 14 both sides
x = 182/14
x = 13
with this calculated value of x, you can replace in the algebraic expression for the measure of angle ∠A:
m∠A = 7x + 24 = 7(13) + 24 = 91 + 24 = 115
Hence, the measure of angle ∠A is m∠A = 115°