Answer:
∠A = 47 deg
∠B = 43 deg
∠C = 124.82 deg
∠D = 55.18 deg
Step-by-step explanation:
recall that by definition:
Complementary angles : add up to 90 deg
Supplementary angles: add up to 180 deg
for ∠A and ∠B, they are complementary, i.e.
∠A + ∠B = 90
(4x+3) + (5x-12) = 90
4x + 3 + 5x - 12 = 90
9x - 9 = 90
9x = 90 + 9
9x = 99
x = 11
hence
∠A = 4x + 3 = 4(11) + 3 = 44+3 = 47 deg
∠B = 90 - 47 = 43 deg
for ∠A and ∠B, they are Supplementary, i.e.
∠C + ∠D = 180
8x-9+3x+5 = 180
x = 16.727 degrees
∠C = 8x - 9 = 8(16.727) - 9 = 124.82
∠D = 180 - 124.82 = 55.18
