In a parallelogram, opposite angles are congruent, which means they have the same measure. Therefore, for parallelogram MART, we have that angle ZA (often denoted as ∠A) is congruent to angle ZR (∠R). Given the expressions for m∠A and m∠R, we can set up an equation based on their congruence:
m∠A = m∠R
2(x + 23) = 3x + 4
We will now solve for x:
2x + 46 = 3x + 4
Subtract 2x from both sides:
46 = x + 4
Now, subtract 4 from both sides:
42 = x
So, x = 42.
Now that we have x, we can calculate the measure of angle ZA:
m∠A = 2(x + 23)
m∠A = 2(42 + 23)
m∠A = 2(65)
m∠A = 130°
Since consecutive angles in a parallelogram are supplementary, and angle ZA is consecutive to angle ZT (∠T), their measures should add up to 180°.
m∠T = 180° - m∠A
m∠T = 180° - 130°
m∠T = 50°
So, the measure of angle ZT is 50°.
