Question

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

Lines b, c, d, e are cut by transversal a. Clockwise from top left, the angles formed by lines b and a are blank, (7 x minus 5) degrees, blank, blank; by lines c and a are blank, blank, (10 x + 15 degrees), blank; by lines d and a are (12 x minus 5) degrees, blank, blank, blank; by lines e and a are blank, (8 x minus 25) degrees, blank, blank.
b is parallel to c
b is parallel to d
b is parallel to e
c is parallel to d
c is parallel to e
d is parallel to e

Answer 1

b is parallel to c

b is parallel to d

c is parallel to d

Explanation:

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Answer 2

b||c; c||d; b||d

Explanation:

Substituting 10 for x, in the angle beside b we have

7(10)-5 = 70-5 = 65

In the angle beside c we have

10(10)+15 = 100+15 = 115

In the angle beside d we have

12(10)-5 = 120-5 = 115

In the angle beside we have

8(10)-25 = 80-25 = 55

The angle beside c has a vertical angle on the other side of c. This angle would be same-side interior angles with the angle beside b; this is because they are inside the block of lines made by b and c and on the same side of a, the transversal. These two angles are supplementary; this is because 65+115 = 180. Since these angles are supplementary, this means that b||c.

The angle beside c and the angle beside d would be alternate interior angles; this is because they are inside the block of lines made by c and d and on opposite sides of the transversal. These two angles are congruent; this means that c||d.

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