Answer:
Claim: the angles 4 and 6 are complementary angles, so the sum of the two angles will equal 90 degrees.
Measure of angle 4 = 48.46 degrees = approx. 48 degrees
Measure of angle 6 = 41.56 degrees = approx. 42 degrees
m<4 + m<6 = 90 degrees
(3x + 31) + (8x - 5) = 90
11x + 26 = 90
11x = 64
x = 64/11
x = 5.82
m<4 = 3x + 31
m<4 = 3(5.82) + 31
m<4 = 17.46 + 31
m<4 = 48.46
m<6 = 8x - 5
m<6 = 8(5.82) - 5
m<6 = 46.56 - 5
m<6 = 41.56
48.46 + 41.56 = 90.02 = approx. 90 degrees