Question

visit www.bigideasmathvideos.com to watch the flipped video instruction for the \try this\ problem try this video for extra example 5 - using properties of parallel lines 4) 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?

Explanation:

Step1: Identify parallel lines property

The horizontal lines (from balloon and ground) are parallel, and the line of sight is a transversal. $\angle 1$ and $\angle 2$ are alternate interior angles.

Step2: Apply alternate interior angles theorem

For parallel lines cut by a transversal, alternate interior angles are congruent.
$m\angle 2 = m\angle 1$

Step3: Substitute given angle value

$m\angle 2 = 37^\circ$

Answer:

$m\angle 2 = 37^\circ$. $\angle 1$ and $\angle 2$ are alternate interior angles formed by a transversal cutting two parallel horizontal lines, so they are congruent.