Question

Which statements about the diagram are true? Select three options.

x = 63
y = 47
z = 117
x + y = 180
x + z = 180
2 horizontal and parallel lines are intersected by 2 diagonal lines to form a triangle with exterior angles. The top angle of the triangle is 47 degrees. The exterior angle created by the right side of the triangle and the top horizontal line is x degrees. The bottom left angle of the triangle is y degrees. The exterior angle of the bottom right angle is z degrees above the horizontal line and 63 degrees below.

Answer 1

True statements: x = 63, z = 117, and x + z = 180.

Reasoning (brief):
- The right diagonal crosses two parallel horizontal lines, so the angle it makes above the top line (x) equals the corresponding 63° angle below the bottom line => x = 63.
- At the bottom-right vertex the angles above and below the horizontal are a linear pair, so z + 63 = 180 ⇒ z = 117.
- Then x + z = 63 + 117 = 180, so x + z = 180 is true.
- Also by the exterior-angle theorem z = 47 + y ⇒ y = 117 − 47 = 70, so y ≠ 47 and x + y ≠ 180.