Question

∠a and ∠b are the same. the measure of ∠c is 21° greater than the measure of ∠a, and the measure of ∠d is 53° less than ∠b. find the measure of ∠a, ∠b, ∠c, and ∠d.

Answer 1

∠ a: x

∠ b: x

∠ c: x + 21

∠ d: x - 53

∠ a + ∠ b + ∠ c + ∠ d = 360 sum of the angles of a rectangle is 360°

(x) + (x) + (x + 21) + (x - 53) = 360

4x - 32 = 360

4x = 392

x = 98

∠ c: x + 21 = (98) + 21 = 119

∠ d: x - 53 = (98) - 53 = 45

Answer: ∠ a = 98°, ∠ b = 89°, ∠ c = 119°, ∠ d = 45°