Question

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try this video for extra example 5 - using properties of parallel lines

1. a balloonist sees a car at a 37° angle of depression from horizontal.

in the diagram, m∠1 = 37°. what is m∠2? how do you know?
∠1 and ∠2 are alternate interior angles
m∠2 = m∠1
m∠1 = 37°
m∠2
m∠2 = 37°

Explanation:

Step1: Identify the relationship between ∠1 and ∠2

Since the lines are parallel (the horizontal lines), ∠1 and ∠2 are alternate interior angles.

Step2: Use the Alternate Interior Angles Theorem

By the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, then alternate interior angles are congruent. So \(m\angle2 = m\angle1\).

Step3: Substitute the value of \(m\angle1\)

Given \(m\angle1 = 37^{\circ}\), substituting into \(m\angle2 = m\angle1\), we get \(m\angle2=37^{\circ}\).

Answer:

\(m\angle2 = 37^{\circ}\) because ∠1 and ∠2 are alternate interior angles formed by parallel lines and a transversal, and by the Alternate Interior Angles Theorem, they are congruent.