Question

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

A. m∠1 = 81° and m∠2 = 99°

B. m∠3 = 99° and m∠4 = 99°

C. m∠2 = 99° and m∠4 = 99°

D. m∠4 = 81° and m∠1 = 81°

Answer 1

(C)

Explanation:

Let us consider that c is parallel to d and p is the transversal, then using the properties of parallel lines, we have

`{\angle}2={\angle}4` ( By alternate exterior angles)

and
`{\angle}2={\angle}3` (By corresponding angles)

From the given options,
`{\angle}2={\angle}4=99^(\circ)`

Thus, the set of equation to prove that lines c and d are parallel lines cut by transversal p is (C) m∠2 = 99° and m∠4 = 99°

Hence, option (C) is correct.

Answer 2

we know that

if c and d are parallel lines

then

m∠2=m∠4 -------> by alternate exterior angles

m∠2=m∠3 -------> by corresponding angles

therefore

the answer is the option C

m∠2 = 99° and m∠4 = 99°