Question

Lines m and n are parallel.

Lines m and n are parallel. Lines s and t intersect lines m and n to form a triangle. The top angle of the triangle is (2 x) degrees. At the intersection of lines s and n, the top left angle is 100 degrees. At the intersection of lines n and 7, the bottom left angle is 70 degrees.


What is the value of x?
10
15
30
35

Answer 1

x = 15

Reason: The two base angles of the triangle are the supplement/corresponding angles to the given ones. The angle at s∩n (top left) is 100°, so the triangle's left base angle is 180 − 100 = 80°. The angle given at t∩n (bottom left) corresponds to the triangle's right base angle of 70°. Thus the base angles add to 80 + 70 = 150°, so the top angle is 180 − 150 = 30°. Since the top angle = 2x, 2x = 30 and x = 15.