Question

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

x = 63
y = 47
z = 117
x + y = 180
x + z = 180

Answer 1

Answers: x = 63 (true), z = 117 (true), x + z = 180 (true).

Reasoning (brief):
- z and 63 are a linear pair on the straight horizontal, so z = 180 − 63 = 117.
- The two horizontal lines are parallel, so the angle the right diagonal makes with the top horizontal (x) is equal to the corresponding angle 63 on the bottom, hence x = 63.
- Then the triangle interior angles are 47 (top) + (interior bottom right) + y = 180. The interior bottom right = 180 − z = 63, so y = 180 − 47 − 63 = 70 (so y = 47 is false). Also x + y ≠ 180, while x + z = 63 + 117 = 180 (true).