Question

in the diagram, m || n. what is the value of x? a. 32 b. 40 c. 52 d. 64 e. 74

Explanation:

Step1: Find the interior - angle related to 148°

The angle adjacent to 148° on the same - side of the transversal and between the parallel lines is 180 - 148=32°.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the triangle formed, we have one angle 20° and another 32°. Let the third angle be \(x\). Then \(x + 20+32 = 180\).

Step3: Solve for \(x\)

\(x=180-(20 + 32)=128\) (This is wrong. Let's use another approach).

Let's use the property of parallel lines and transversals.

Step1: Extend the lines

Draw a line parallel to \(m\) and \(n\) passing through the vertex of the angle \(x\).

Step2: Use the alternate - interior angles property

The angle corresponding to the 20° angle and the angle corresponding to the angle adjacent to 148° (which is \(180 - 148=32^{\circ}\)) are formed.
The angle \(x\) is the sum of these two non - overlapping angles formed by the parallel lines and the transversals.
So \(x=20+(180 - 148)\)
\(x=20 + 32=52\)

Answer:

C. 52