Question

In the figure p || q. Find < mPLEASE HELPPP!

Answer 1

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.