Question

question 5: two parallel lines are cut by a transversal. suppose ( mangle8 = 33^{circ} ). find ( mangle2 ) & ( mangle3 ). ( mangle2= ) ( mangle3= ) question 6: find ( mangle lpn ) if ( angle3 ) is a right angle and ( angle mpncongangle rpn )

Explanation:

Step1: Find \(m\angle2\)

When two parallel lines are cut by a transversal, \(\angle2\) and \(\angle8\) are alternate - exterior angles. By the Alternate - Exterior Angles Theorem, if two parallel lines are cut by a transversal, then alternate - exterior angles are congruent. So \(m\angle2=m\angle8\). Given \(m\angle8 = 33^{\circ}\), then \(m\angle2=33^{\circ}\).

Step2: Find \(m\angle3\)

\(\angle2\) and \(\angle3\) are supplementary angles (they form a linear pair). By the definition of supplementary angles, \(m\angle2 + m\angle3=180^{\circ}\). Since \(m\angle2 = 33^{\circ}\), we substitute into the equation: \(33^{\circ}+m\angle3=180^{\circ}\). Then \(m\angle3=180^{\circ}-33^{\circ}=147^{\circ}\).

Answer:

\(m\angle2 = 33^{\circ}\), \(m\angle3=147^{\circ}\)