Question

find the measure of each angle indicated. 19) 20) 21) 22)

Explanation:

1. For the first - type of parallel - line and transversal problem (assuming the lines are parallel):

• 19):
• # Explanation:

Step1: Use the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are equal. If one of the angles formed by the transversal and the parallel lines is \(77^{\circ}\), and the angle we need to find is a corresponding angle, then the measure of the indicated angle is equal to the given angle.
Let the indicated angle be \(x\). Since the lines are parallel and the angles are corresponding, \(x = 77^{\circ}\).

• # Answer:

\(77^{\circ}\)

• 20):
• # Explanation:

Step1: Use the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are equal. Given an angle of \(89^{\circ}\), and the indicated angle is a corresponding angle to it. Let the indicated angle be \(y\). Then \(y=89^{\circ}\) because of the corresponding - angle property for parallel lines and a transversal.

• # Answer:

\(89^{\circ}\)

• 21):
• # Explanation:

Step1: Use the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are equal. Given an angle of \(68^{\circ}\), and the indicated angle is a corresponding angle. Let the indicated angle be \(z\). Then \(z = 68^{\circ}\) due to the corresponding - angle relationship in parallel - line and transversal geometry.

• # Answer:

\(68^{\circ}\)

• 22):
• # Explanation:

Step1: Use the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are equal. Given an angle of \(55^{\circ}\), and the indicated angle is a corresponding angle. Let the indicated angle be \(w\). Then \(w=55^{\circ}\) as corresponding angles formed by parallel lines and a transversal are congruent.

• # Answer:

\(55^{\circ}\)

Answer:

1. For the first - type of parallel - line and transversal problem (assuming the lines are parallel):

• 19):
• # Explanation:

Step1: Use the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are equal. If one of the angles formed by the transversal and the parallel lines is \(77^{\circ}\), and the angle we need to find is a corresponding angle, then the measure of the indicated angle is equal to the given angle.
Let the indicated angle be \(x\). Since the lines are parallel and the angles are corresponding, \(x = 77^{\circ}\).

• # Answer:

\(77^{\circ}\)

• 20):
• # Explanation:

Step1: Use the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are equal. Given an angle of \(89^{\circ}\), and the indicated angle is a corresponding angle to it. Let the indicated angle be \(y\). Then \(y=89^{\circ}\) because of the corresponding - angle property for parallel lines and a transversal.

• # Answer:

\(89^{\circ}\)

• 21):
• # Explanation:

Step1: Use the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are equal. Given an angle of \(68^{\circ}\), and the indicated angle is a corresponding angle. Let the indicated angle be \(z\). Then \(z = 68^{\circ}\) due to the corresponding - angle relationship in parallel - line and transversal geometry.

• # Answer:

\(68^{\circ}\)

• 22):
• # Explanation:

Step1: Use the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are equal. Given an angle of \(55^{\circ}\), and the indicated angle is a corresponding angle. Let the indicated angle be \(w\). Then \(w=55^{\circ}\) as corresponding angles formed by parallel lines and a transversal are congruent.

• # Answer:

\(55^{\circ}\)