In the diagram, m∠A=(4x−10)° and m∠D=(2x+22)° . What is the measure of ∠D ?

Answer 1

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}.