Question

Given a∥b , and c is not parallel to a or b, which statements must be true?

Select each correct answer.


m∠3=m∠7

m∠5=m∠9

m∠1=m∠12

m∠1=m∠8

Answer 1

angle 3 = angle 7 and angle 1 = angle 8 are true,.

Step-by-step explanation:

Given two parallel lines a and b. c is not parallel to a or b.

We know that parallel lines never meet. And when a transversal cuts the parallel lines, we have corresponding angles equal and alternate angles equal.

Here when the set of parallel lines a,b are cut by transversal, corresponding

angles formed are (3,7) .

Hence angle 3 = angle 7 ... i

I option is right

Also (4,8) are corresponding angles. Hence

angle 4 = angle 8 (corresponding angles)

angle 1 = angle 4 (vertically opposite angles)

Hence we get angle 1 = angle 8

Option 4 is true.

5 and 9 are not formed by parallel lines hence they need not be equal.

Similarly 1 and 12 need not be equal as c is not parallel to a or b.

SO only option 1 and 4 are correct.

Answer 2

m<3 = m<7 true

m1 = m<8 true

the others are not true since c is not parallel