Question

Which set of equations is enough information to prove that lines c and d are parallel lines cut by transversal p?

m∠1 = 81° and m∠2 = 99°

m∠3 = 99° and m∠4 = 99°

m∠2 = 99° and m∠4 = 99°

m∠4 = 81° and m∠1 = 81°

Answer 1

The correct answer isC) m∠2 = 99° and m∠4 = 99°
Hope this helps you!

Answer 2

Answer:

Option C is the right answer.

Step-by-step explanation:

m∠2 = 99° and m∠4 = 99° is the equation enough to prove that lines c and d are parallel lines cut by transversal p.

For two lines to be parallel and cut by a transverse, let us construct a diagram, where  

Let line c be AB  

lined be JK

The transverse p be XY

From the given diagram, 2 parallel lines AB and JK, which is cut by a transverse line XY,

We can see that, among the 4 angles marked 1, 2, 3 and 4,  

1 and 3 are Vertically Opposite Angles and 2 and 4 are Vertically Opposite Angles.

Hence, for two lines to be parallel and cut by a transverse, the Vertically Opposite Angles must be equal.

From all the given options, only the 3rd option shows that m∠2 = 99° and m∠4 = 99°, which are equal Vertically Opposite Angles.

Hence the information which is enough is that m∠2 = 99° and m∠4 = 99°.