Question

note: figure not drawn to scale.
in the figure, line ab is parallel to line cd, and line ad intersects line bc at point e. if y = 118 and z = 116, what is the value of x?
a 54
b 64
c 126
d 144

Explanation:

Step1: Find the measure of the angle adjacent to \( y \)

Since \( y = 118^{\circ} \), the adjacent angle \( \angle ABE=180 - 118=62^{\circ} \) (linear - pair of angles: \( \angle ABE+y = 180^{\circ} \)).

Step2: Find the measure of the angle adjacent to \( z \)

Since \( z = 116^{\circ} \), the adjacent angle \( \angle CDE=180 - 116 = 64^{\circ} \) (linear - pair of angles: \( \angle CDE+z = 180^{\circ} \)).

Step3: Use the property of parallel lines and the exterior - angle theorem

Because \( AB\parallel CD \), and \( AD \) and \( BC \) are transversals.
In \( \triangle ABE \) and \( \triangle DCE \), by the exterior - angle theorem of a triangle \( x=\angle ABE+\angle CDE \) (the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles).
Substitute \( \angle ABE = 62^{\circ} \) and \( \angle CDE=64^{\circ} \) into the formula: \( x=62 + 64=126^{\circ} \)

Answer:

C. 126