In the diagram, m∠A=(4x−10)° and m∠D=(2x+22)° . What is the measure of ∠D ?
Since ∠A and ∠D are vertical angles, they are congruent. Thus,
(4x - 10)° = (2x + 22)°
Subtracting 2x from both sides, we get:
2x - 10 = 22
Adding 10 to both sides, we get:
2x = 32
Dividing both sides by 2, we get:
x = 16
Substituting x = 16 back into the equation for ∠D, we get:
∠D = 2x + 22 = 2(16) + 22 = 32 + 22 = 54
Therefore, the measure of ∠D is 54 degrees. Answer: \boxed{54}.