Question

Ethan is proving the Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Given: Triangle ABC on line segment AD

Prove: m∠ A + m∠ B = m∠ BCD

https://imgur.com/ApDR6tL

https://imgur.com/Vgqc1mb

What statement should Ethan add at Step 5 to complete the proof?

A. m∠ BCA+ m∠BCD = 90°

B. m∠ BCA= m∠BCD

C. m∠ BCA+ m∠BCD = 180°

D. m∠ BCA< m∠BCD

Answer 1

@SmokeyBrown

Answer 2

@563blackghost

Answer 3

Supplementary angles are always equal to 180

Answer 4

C ?

Answer 5

Yep

Answer 6

Darnelle drew this figure and the accompanying equations.

https://imgur.com/wbx0fDq

w + x + y = 180
y + z = 180

Which equation must also be true?

A. w + z = 180


B. w + x + z = 180


C. y – x = w


D. w + x = z