In the diagram, m∠A=(4x−10)° and m∠D=(2x+22)° . What is the measure of ∠D ? (1 point)g
To find the measure of ∠D, we need to use the information given in the diagram that m∠A=(4x−10)° and m∠D=(2x+22)°.
Since ∠A and ∠D are supplementary angles (they add up to 180°), we can set up the equation:
m∠A + m∠D = 180
Substitute the given values into the equation:
(4x-10) + (2x + 22) = 180
Combine like terms:
6x + 12 = 180
Subtract 12 from both sides:
6x = 168
Divide by 6:
x = 28
Now, substitute x back into the expression for ∠D:
m∠D = 2(28) + 22
m∠D = 56 + 22
m∠D = 78
Therefore, the measure of ∠D is 78°.