Question

If x=10 which lines are parallel? Check all that apply.

1. B||C
2.B||D
3.B||E
4.C||D
5.C||E
6.D||E

Answer 1

B||C, and B||D

Explanation:

Hoped this helped

Answer 2

1. B||C

2.B||D

4.C||D

Explanation:

Substituting 10 in for x, the angle next to line b is

7(10)-5 = 70-5 = 65°.

The angle next to line c is

10(10)+15 = 100+15 = 115°.

The angle next to line d is

12(10)-5 = 120-5 = 115°.

The angle next to line e is

8(10)-25 = 80-25 = 55°.

The angle next to line c and the angle next to line d are alternate interior angles. They are inside lines c and d and on opposite sides of line a, the transversal. Since these two angles are congruent, this means that c || d.

The angle adjacent to the angle beside line c would need to be

180-115 = 65°. This is because these are a linear pair, and must sum to 180°.

This angle is a corresponding angle to the angle beside line b; since they are congruent, this tells us that b || c.

Since c || d and b || c, using the transitive property, b || d.