a) What is true about the angle pair ∠A and ∠D and angle pair ∠B and ∠C is that they are supplementary angles.
b) The value of the missing angle m∠D is 70°
How to find the angles of a trapezium?
Two angles on the same side of a trapezoid are supplementary, that is the sum of the angles of two adjacent sides is equal to 180°.
Thus:
∠A + ∠D = 180°
Similarly:
∠B + ∠C = 180°
We are given:
m∠A = 5x - 15
m∠B = 5x - 2
m∠C = 2x + 7
Thus:
5x - 2 + 2x + 7 = 180
7x + 5 = 180
7x = 175
x = 25
m∠A = 5(25) - 15
m∠A = 110°
m∠D = 180° - 110°
m∠D = 70°