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 = 115 ) and ( z = 117 ), what is the value of ( x )?
a 52
b 63
c 128
d 142

Explanation:

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

Since \( y = 115^{\circ} \), the adjacent angle to \( y \) is \( 180 - 115=65^{\circ} \) (linear - pair angles: \( a + b=180^{\circ} \)).

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

Since \( z = 117^{\circ} \), the adjacent angle to \( z \) is \( 180 - 117 = 63^{\circ} \) (linear - pair angles: \( a + b = 180^{\circ} \)).

Step3: Use the triangle - angle - sum property

In the triangle formed, let the three angles be \( A = 65^{\circ}\), \( B = 63^{\circ}\), and \( C=x^{\circ}\) (where \( C \) is the exterior angle of the triangle).
By the exterior - angle property of a triangle (the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles), \( x=65 + 63\).

Answer:

\( x = 128\), so the answer is C.