Question

In the figure below, lines m and n are parallel. What is the measure of angle y?

Answer 1

B

Explanation:

y and
`(1)/(2)` x + 20 are corresponding angles and are congruent, then

y =
`(1)/(2)` x + 20 → (1)

2x - 10 and y are adjacent angles and supplementary, sum to 180°, so

2x - 10 +
`(1)/(2)` x + 20 = 180, that is

`(5)/(2)` x + 10 = 180 ( subtract 10 from both sides )

`(5)/(2)` x = 170 ( multiply both sides by 2 to clear the fraction )

5x = 340 ( divide both sides by 5 )

x = 68

Substitute x = 68 into (1)

y =
`(1)/(2)` (68) + 20 = 34 + 20 = 54° → B