Questions: Prove that the measures of the exterior angles of a triangle have a sum of 360°.
Given: angle 1, angle 2, and angle 3 are exterior angles.
Prove: m angle 1 + m angle 2 + m angle 3 = 360
It is given that angle 1, angle 2, and angle 3 are exterior angles.
Transcript text: Prove that the measures of the exterior angles of a triangle have a sum of $360^{\circ}$.
Given: $\angle 1, \angle 2$, and $\angle 3$ are exterior angles.
Prove: $m \angle 1+m \angle 2+m \angle 3=360$
It is given that $\angle 1, \angle 2$, and $\angle 3$ are exterior angles.
Solution
Solution Steps
Step 1: Identify the Exterior Angles
Given that ∠1, ∠2, and ∠3 are exterior angles of the triangle.
Step 2: Apply the Triangle Exterior Angle Theorem
By the Triangle Exterior Angle Theorem, each exterior angle is equal to the sum of the two non-adjacent interior angles. Therefore:
m∠1 = 180° - m∠A
m∠2 = 180° - m∠B
m∠3 = 180° - m∠C
Step 3: Sum of Exterior Angles
The sum of the measures of the exterior angles of a triangle is:
m∠1 + m∠2 + m∠3 = (180° - m∠A) + (180° - m∠B) + (180° - m∠C)