Question

the exterior angle is ∠4. the non - adjacent interior angles are ∠1 and ∠2. m∠3 + m∠4 = 180° m∠1 + m∠2 + m∠3 = 180° isolate m∠4 in the equation. m∠3 + m∠4 = m∠1 + m∠2 + m∠3 m∠4 = ?

Explanation:

Step1: Subtract \( m\angle3 \) from both sides

Given the equation \( m\angle3 + m\angle4 = m\angle1 + m\angle2 + m\angle3 \), we subtract \( m\angle3 \) from each side.

$$ m\angle3 + m\angle4 - m\angle3 = m\angle1 + m\angle2 + m\angle3 - m\angle3 $$

Step2: Simplify both sides

Simplifying the left side: \( m\angle3 - m\angle3 + m\angle4 = m\angle4 \).
Simplifying the right side: \( m\angle1 + m\angle2 + (m\angle3 - m\angle3) = m\angle1 + m\angle2 \).

Answer:

\( m\angle1 + m\angle2 \)