Question

22:17
hide
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 = 117 and z = 114, what is the value of x?
a 51
b 66
c 129
d 141

Explanation:

Step1: Find the adjacent - angle of \(y\)

Since \(y = 117\), the adjacent - angle of \(y\) (let's call it \(\angle ABE\)) is \(180 - y\).

$$180 - 117=63$$

Step2: Find the adjacent - angle of \(z\)

Since \(z = 114\), the adjacent - angle of \(z\) (let's call it \(\angle CDE\)) is \(180 - z\).

$$180 - 114 = 66$$

Step3: Use the triangle - angle - sum property

In \(\triangle ABE\) and \(\triangle CDE\) (because \(AB\parallel CD\), we can use the property of angles in a triangle. In \(\triangle ABE\) and \(\triangle CDE\), we know that in \(\triangle ABE\) and \(\triangle CDE\) (by the property of parallel lines and transversals, the angles we found are interior angles of \(\triangle ABE\) and \(\triangle CDE\)). In \(\triangle ABE\) and \(\triangle C DE\), for \(\triangle ABE\) and \(\triangle CDE\) (using the fact that the sum of angles in a triangle is \(180^{\circ}\)).
We know that \(x=180-(63 66)\)

$$x = 180-(63 + 66)=51$$

Answer:

A. 51