Question

in the diagram, lines ( t ) and ( m ) are cut by transversals ( n ) and ( p ).
part a
enter the measure of ( angle 1 ) degree
part b
enter the measure of ( angle 2 ) degree

Explanation:

Step1: Find the measure of \(\angle1\)

Since \(\angle1\) and the \(59^{\circ}\) angle are alternate - interior angles (lines \(l\) and \(m\) are parallel and \(n\) is a transversal), \(\angle1 = 59^{\circ}\) (alternate - interior angles are congruent).

Step2: Find the measure of \(\angle2\)

Lines \(l\) and \(m\) are parallel, and \(p\) is a transversal. The angle adjacent to the \(59^{\circ}\) angle and the right - angle (\(90^{\circ}\)) form a linear - pair with \(\angle2\) (using the property of parallel lines and transversals).
First, find the angle adjacent to the \(59^{\circ}\) angle. Let's call it \(x\). Since \(x + 59^{\circ}=90^{\circ}\) (complementary angles in the right - angled situation related to parallel lines), \(x = 90^{\circ}-59^{\circ}=31^{\circ}\).
Then, \(\angle2\) and \(x\) are alternate - interior angles. So \(\angle2=31^{\circ}\) (alternate - interior angles are congruent).

Answer:

Part A: \(59\)
Part B: \(31\)