Question

the figure shows a triangle with unknown angles. which equation shows the relationship between the exterior angle and the interior angles? m∠2 = m∠1 + m∠4; m∠2 = m∠3 + m∠4; m∠4 = m∠1 + m∠2; m∠4 = m∠2 + m∠3

Explanation:

Step1: Recall Exterior Angle Theorem

The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Identify Angles in the Triangle

In the given triangle, \(\angle4\) is an exterior angle. The two non - adjacent interior angles to \(\angle4\) are \(\angle1\) and \(\angle2\). So, by the Exterior Angle Theorem, \(m\angle4=m\angle1 + m\angle2\).

Answer:

\(m\angle4 = m\angle1 + m\angle2\) (the third option: \(m\angle4 = m\angle1 + m\angle2\))