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 10, because the angles shown in the diagram are complementary angles. the value of x is 80, because the angles shown in the diagram are congruent angles. the value of x is 170, because the measures of the angles shown in the diagram add up to 270° and 170 + 100 = 270. the value of x is 100, because the angles shown in the diagram have equal measures.

Explanation:

Step1: Identify angle - type relationship

When two parallel lines are cut by a transversal, corresponding angles are congruent. The \(100^{\circ}\) angle and the \(x^{\circ}\) angle are corresponding angles.

Step2: Determine the value of \(x\)

Since corresponding angles are equal, \(x = 100\).

Answer:

The value of \(x\) is 100, because the angles shown in the diagram have equal measures.