Answer:
x = 37
Explanation:
Pre-Solving
We are given parallelogram ABCD.
We know that m∠A = 22° and m∠D = 4x + 10 degrees.
We want to find the value of x.
Recall that a parallelogram is made up of 2 pairs of parallel sides. This means line segment AB ║ line segment DC and line segment AD ║ line segment BC
Because AB ║ DC, the line between the two (AD) is a transversal, so ∠A and ∠D are same-side interior angles.
Recall that same-side interior angles equal 180° when added together. So, m∠A + m∠D = 180
We can substitute these values for:
22 + 4x + 10 = 180
Solving
Add like terms together.
32 + 4x = 180
Subtract 32 from both sides.
4x = 148
Divide both sides by 4.
x = 37