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

In the diagram, the transversal creates alternate interior angles with the parallel sides (implied by the horizontal lines and the triangle). $\angle 2$ and $\angle 5$ are alternate interior angles, so they are congruent.

Step2: Conclude Angle Measure Relationship

By the alternate interior angles theorem, $m\angle 2 = m\angle 5$.

Answer:

$m\angle 5$ (or specifically, $m\angle 2 = m\angle 5$)