Question

13 mark for review 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 = 113 and z = 116, what is the value of x? a 49 b 64 c 131 d 139

Explanation:

Step1: Find the interior - angle related to y

Since \(AB\parallel CD\), the angle adjacent to \(y\) inside the triangle formed by \(E\) has a measure of \(180 - y\). Given \(y = 113\), then \(180 - y=180 - 113 = 67\).

Step2: Find the other interior - angle related to z

The angle adjacent to \(z\) inside the triangle formed by \(E\) has a measure of \(180 - z\). Given \(z = 116\), then \(180 - z=180 - 116 = 64\).

Step3: Use the angle - sum property of a triangle

In a triangle, the sum of the interior angles is \(180^{\circ}\). Let the three interior angles of the triangle at \(E\) be \(a\), \(b\), and \(x\). We know \(a = 67\) and \(b = 64\). Then \(x=180-(67 + 64)\).
\[x=180-(67 + 64)=180 - 131=49\]

Answer:

A. 49