Question

The diagram shows two parallel lines and transversal. If the measure of <6 is 140, what is the measure of <1?

Answer 1

Angles 6 and 3 are supplementary. If angle 6 is 140, then angle 3 is 40. Because those lines are parallel and cut by a transversal, then angles 3 and 1 are corresponding and congruent. That means that angle 1 measures 40° also. Choice D.

Answer 2

(D)

Explanation:

Given: It is given that ∠6 measures 140°.

To find: The measure of ∠1.

Solution:

It is given that ∠6 measures 140° and since there are two parallel lines which are cut by a transversal, then using the properties of parallel lines, we have

m∠6=m∠2(Alternate interior angles)

Therefore, m∠6=m∠2=140°

Also, m∠2 and m∠1 forms the linear pair, therefore

m∠1+m∠2=180°(Linear pair)

⇒m∠1+140°=180°

⇒m∠1=180-140

⇒m∠1=40°

Thus, the measure of ∠1 is 40°.

Hence, option D is correct.