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In the figure p || q. Find < m
PLEASE HELPPP!

In the figure p || q. Find < m PLEASE HELPPP!-example-1
User Ron Gross
by
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1 Answer

4 votes

Option B:

m∠1 = 70°

Solution:

The reference image is attached below.

Extend the line v and t which intersect at p and q respectively.

To find the measure of angle ASB:

Sum of the angles in a straight line = 180°


m \angle A S B+116^(\circ)=180^(\circ)


m \angle A S B=180^(\circ)-116^(\circ)


m \angle A S B=64^(\circ)

Given p || q and 134° and ∠SBC are corresponding angles.

If two lines are parallel, then the corresponding angles are congruent.

∠SBC = 134°

∠SBA and ∠SBC form a linear pair.

∠SBA + ∠SBC = 180°

∠SBA + 134° = 180°

∠SBA = 46°

Sum of the interior angles of the triangle is 180°.

In ΔSAB,


m \angle A S B+m \angle S A B+m \angle S B A=180^(\circ)


64^(\circ)+m \angle S A B+46^(\circ)=180^(\circ)


m \angle S A B=180^(\circ)-110^(\circ)


m \angle S A B=70^(\circ)

∠1 and ∠SAB are vertical angles.

Vertical angles are congruent.

m∠1 = m∠SAB

m∠1 = 70°

Option B is the correct answer.

In the figure p || q. Find < m PLEASE HELPPP!-example-1
User Solarissmoke
by
4.0k points