Question

the figure shown is a triangle with three unknown angles. to find out if the sum of the three interior angle measures of any triangle is 180°, show: m∠1 + m∠2 + m∠3 = 180° use the transversal to find a relationship. which angle has the same measure as ∠1? m∠1 = m∠4 which angle has the same measure as ∠2? m∠2 = ?

Explanation:

Step1: Identify Alternate Interior Angles

The lines are parallel (the two horizontal lines), and the purple line is a transversal. For ∠2, the alternate interior angle with respect to the transversal is ∠5. So by the Alternate Interior Angles Theorem, \( m\angle2 = m\angle5 \).

Answer:

\( m\angle5 \)