Question

in the diagram below, line m is parallel to line n, and line t intersects lines m and n. based on the diagram, which of the following statements is true? the value of x is 95, because the angles shown in the diagram are acute angles. the value of x is 95, because the angles shown in the diagram have the same measure. the value of x is 85, because the angles shown in the diagram are supplementary angles. the value of x is 85, because the angles shown in the diagram are obtuse angles.

Explanation:

Step1: Identify angle - relationship

When two parallel lines \(m\) and \(n\) are intersected by a transversal \(t\), the angles shown are corresponding angles.

Step2: Recall angle - property

Corresponding angles are congruent. So \(x = 95\) since the given angle of \(95^{\circ}\) and the angle \(x^{\circ}\) are corresponding angles.

Answer:

The value of \(x\) is 95, because the angles shown in the diagram have the same measure.