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Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measure.

m∠1=(50x−50)∘, m∠2=(20x+70)∘
Alt. Ext. ∠s Thm.
m∠1 = 130°, m∠2 = 130°

Same-Side Int. ∠s Thm.
m∠1 = 130°, m∠2 = 130°

Alt. Int. ∠s Thm.
m∠1 = 150°, m∠2 = 150°

Corr. ∠s Post.
m∠1 = 150°, m∠2 = 150°

Sagot :

akposevictor

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°

Learn more about the corresponding angles postulate on:

https://brainly.com/question/2938476

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