Question

select the correct answer.
in the figure, lines m and n are parallel to each other. lines p and q are also parallel to each other. what is the value of x?
a. 40°
b. 80°
c. 100°
d. 180°

Explanation:

Step1: Use the property of adjacent angles

Adjacent angles on a straight - line sum to \(180^{\circ}\). Let the angle adjacent to the \(100^{\circ}\) angle be \(y\). Then \(y + 100^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-100^{\circ}=80^{\circ}\).

Step2: Use the property of parallel lines

Since lines \(m\) and \(n\) are parallel and lines \(p\) and \(q\) are parallel, by the property of parallel lines (corresponding angles or alternate - interior angles), \(x=y\).

Answer:

B. \(80^{\circ}\)