The theorem used and the angle measures are:
D. corresponding angles postulate
m∠1 = 150°, m∠2 = 150°
What is the Corresponding Angles Postulate?
According to the corresponding angles postulate, if two angles lie on same relative corner along a transversal that cuts two parallel lines (corresponding angles), then their measures are equal.
Thus, ∠1 and ∠2 are corresponding angles, therefore:
m∠1 = m∠2 [corresponding angles postulate]
Given the following:
m∠1 = (50x − 50)∘,
m∠2 = (20x + 70)∘
Therefore, we would have:
50x − 50 = 20x + 70
Subtract 20x from both sides
50x − 50 - 20x = 20x + 70 - 20x
30x − 50 = 70
Add 50 to both sides of the equation
30x − 50 + 50 = 70 + 50
30x = 120
Divide both sides by 30
30x/30 = 120/30
x = 4
Plug in the value of x
m∠1 = (50x − 50) = 50(4) − 50 = 150°
m∠2 = (20x + 70)∘ = 20(4) + 70 = 150°
Thus, the answer is: D. corresponding angles postulate
m∠1 = 150°, m∠2 = 150°
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