Question

complete each step to show that m∠3 + m∠2 = m∠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 = m∠4 + m∠1 ← both sums equal 180°.
m∠3 + m∠2 = m∠4 ← subtract ? from both sides.

Explanation:

Step1: Identify common term

In the equation \( m\angle3 + m\angle2 + m\angle1 = m\angle4 + m\angle1 \), the common term on both sides is \( m\angle1 \).

Step2: Subtract common term

To isolate \( m\angle3 + m\angle2 \) and \( m\angle4 \), we subtract \( m\angle1 \) from both sides. This follows the subtraction property of equality, which states that if \( a + c = b + c \), then \( a = b \) (here \( a = m\angle3 + m\angle2 \), \( b = m\angle4 \), and \( c = m\angle1 \)).

Answer:

\( m\angle1 \)