Question

Use the marked parallel lines to find the value of Y in the diagram below.

A) 19
B) 50
C) 55
D) 18

Answer 1

A) 19

Explanation:

3x - 45 = 2x + 5 (alternate interior angles are the same)

→ 3x -2x = -45 + 5 (collecting x terms on LHS and constant on RHS)

→ x = 50

we also have

(4y-1) + (2x-5) = 180 (consecutive interior angles add to 180°

⇒ 2x + 4y -1 + 5 = 180

⇒ 2x + 4y + 4 = 180

⇒ 2x + 4y = 180-4 = 176

Substituting for x = 50

2(50) + 4y = 176

⇒100 + 4y = 176

⇒ 4y = 176-100 = 76

⇒ y = 76/4 = 19

Answer 2

A) 19

Explanation:

as the angles between intersecting lines are the same at the top and the bottom of such a line (just mirrored left/right), and parallel lines intersect with the same angles, we have

2x + 5 = 3x - 45

5 = x - 45

x = 50

4y - 1 is the supplementary angle (together they have 180°) to e.g. 2x + 5, because the sum of all angles around a single point on one side of a line is always 180° (one side of a line represents a half-circle = 180°).

2x + 5 = 2×50 + 5 = 105°

4y - 1 + 105 = 180

4y + 104 = 180

4y = 76

y = 19