In the diagram, m∠A=(4x−10)° and m∠D=(2x+22)°. What is the measure of ∠D?
We are given that m∠A = (4x - 10)° and m∠D = (2x + 22)°. We want to find the measure of ∠D.
Since we know the measure of ∠D is (2x + 22)°, we can set up the equation:
(2x + 22)° = ∠D
Now we can substitute this equation into the equation for ∠A:
m∠A = (4x - 10)°
(4x - 10)° = (2x + 22)°
Now we can solve for x:
4x - 10 = 2x + 22
2x = 32
x = 16
Now we can substitute the value of x back into the equation for ∠D:
(2x + 22)° = (∠D)°
(2(16) + 22)° = (∠D)°
(32 + 22)° = (∠D)°
54° = (∠D)°
Therefore, the measure of ∠D is 54 degrees.