In the figure above, lines l and m are parallel, y = 20, and z = 60. What is the value of x ?

Options

A. 120
B. 100
C. 90
D. 80

Answer

B

Explanation

Let the measure of the third angle in the smaller triangle be `a^@`. Since lines l and m are parallel and cut by transversals, it follows that the corresponding angles formed are congruent. So `a^@ = y^@ = 20^@`. The sum of the measures of the interior angles of a triangle is `180^@`, which for the interior angles in the smaller triangle yields a + x + z = 180. Given that z = 60 and a = 20, it follows that 20 + x + 60 = 180. Solving for x gives x = 180 − 60 − 20, or x = 100.
Choice A is incorrect and may result from incorrectly assuming that angles x + z = 180. Choice C is incorrect and may result from incorrectly assuming that the smaller triangle is a right triangle, with x as the right angle. Choice D is incorrect and may result from a misunderstanding of the exterior angle theorem and incorrectly assuming that x = y + z.