Question

1. in the accompanying diagram, line m is parallel to line n and they are cut by transversal t. if the acute angle shown is 15°, which of the following statements is true? (1) m∠x = 15° and is an obtuse angle (2) m∠x = 15° and is an acute angle (3) m∠x = 165° and is an obtuse angle (4) m∠x = 165° and is an acute angle

Explanation:

Step1: Recall angle - relationship

When two parallel lines \(m\) and \(n\) are cut by a transversal \(t\), the sum of adjacent angles on the same - side of the transversal is \(180^{\circ}\).

Step2: Calculate the measure of \(\angle x\)

Let the given acute angle be \(15^{\circ}\). Then \(m\angle x+15^{\circ}=180^{\circ}\), so \(m\angle x = 180^{\circ}-15^{\circ}=165^{\circ}\).

Step3: Classify the angle

An obtuse angle is an angle whose measure is greater than \(90^{\circ}\) and less than \(180^{\circ}\). Since \(90^{\circ}<165^{\circ}<180^{\circ}\), \(\angle x\) is an obtuse angle.

Answer:

(3) \(m\angle x = 165^{\circ}\) and is an obtuse angle