Question

use the image to answer the question
prove that the sum of the measures of the exterior angles of the triangle is 360°. fill in the blanks in step 7 to complete the proof
(1 point)
two - column proof for sum of exterior angles of a triangle is 360 degrees
statement
1 consider a triangle with interior angles ∠2, ∠4, and ∠6 and corresponding exterior angles ∠1, ∠3, and ∠5
2 m∠1 + m∠2 = 180°
m∠5 + m∠6 = 180°
m∠3 + m∠4 = 180°
3 (m∠1 + m∠2)+(m∠5 + m∠6)+(m∠3 + m∠4)=180° + 180° + 180°
4 (m∠2 + m∠4 + m∠6)+(m∠1 + m∠3 + m∠5)=540°
5 m∠2 + m∠4 + m∠6 = 180°
6 180°+(m∠1 + m∠3 + m∠5)=540°
7 (m∠□ + m∠□ + m∠□)=□°

Explanation:

Step1: Analyze the equation from step 6

We have \(180^{\circ}+(m\angle1 + m\angle3 + m\angle5)=540^{\circ}\)

Step2: Apply the Subtraction Property of Equality

Subtract \(180^{\circ}\) from both sides of the equation: \((m\angle1 + m\angle3 + m\angle5)=540^{\circ}- 180^{\circ}\)

Step3: Calculate the right - hand side

\(540^{\circ}-180^{\circ}=360^{\circ}\), so \(m\angle1 + m\angle3 + m\angle5 = 360^{\circ}\)

Answer:

\(m\angle1 + m\angle3 + m\angle5 = 360^{\circ}\)