Question

complete each step to show that m∠3 + m∠2 = m∠4.
(image of a triangle with angles labeled 1, 2, 3, 4)
m∠4 + m∠1 = 180° ← ∠4 and ∠1 are supplementary.
m∠3 + m∠2 + m∠1 = 180° ← a triangle’s interior angles sum to 180°.
m∠3 + m∠2 + m∠1 = ? ← both sums equal 180°.
options: m∠4 + m∠1, m∠4 + m∠2, m∠4 + m∠3

Explanation:

Step1: Analyze given equalities

We know \( m\angle4 + m\angle1 = 180^\circ \) (supplementary angles) and \( m\angle3 + m\angle2 + m\angle1 = 180^\circ \) (triangle interior angles sum).

Step2: Set equal due to same sum

Since both sums equal \( 180^\circ \), we can set \( m\angle3 + m\angle2 + m\angle1 = m\angle4 + m\angle1 \).

Answer:

\( m\angle4 + m\angle1 \)