Question

based on the diagrams, which statement is true? the value of x is 79, because the two angles shown in the diagram are congruent. the value of x is 11, because the two angles shown in the diagram are complementary. the value of x is greater than 90, because the two angles shown in the diagram are obtuse angles. the value of x is 101, because the two angles shown in the diagram are supplementary.

Explanation:

Step1: Recall the property of supplementary angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. That is, if two angles \(a\) and \(b\) are consecutive interior angles, then \(a + b=180^{\circ}\). In the fourth diagram, the angle of \(79^{\circ}\) and \(x^{\circ}\) are consecutive interior angles.

Step2: Set up the equation

We know that \(79 + x=180\) (by the supplementary - angles property for parallel lines cut by a transversal).

Step3: Solve for \(x\)

Subtract \(79\) from both sides of the equation: \(x = 180-79\).

$$x=101$$

Answer:

The value of \(x\) is \(101\), because the two angles shown in the diagram are supplementary.