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If 2/1 = 60°, find the measures of the other angles if the lines / and m are parallel.

If 2/1 = 60°, find the measures of the other angles if the lines / and m are parallel-example-1

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We have a transversal with two parallel lines:

If ∠1 =60°

∠1 = ∠8 using the alternate exterior angles property.

Also

∠1 =∠4 and ∠8 = ∠5 using the corresponding angles ( they are vertical angles)

Now, ∠1 and ∠2 are supplementary angles, they together form a right line.

Supplementary angles are equal to 180°, then, we can deduce the next equation:

∠1 + ∠2 = 180°

Replacing ∠1 = 60°

60° + ∠2 = 180°

Solve for ∠2:

∠2 = 180° - 60°

∠2 = 120°

Then ∠2 = ∠7 using the alternate exterior angles property.

Also

∠7 = ∠6 and ∠2 = ∠3

So far we got:

∠1 = ∠4 = ∠5 = ∠8 = 60°

and

∠2 = ∠3 = ∠6 = ∠7 = 120°

Therefore, the correct answer is the third option.

User Koronis Neilos
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