SOLUTION: I do nit understand how to solve proofs. I have a proof that given triangle abc with exterior angle angle acd and the given is the measure of angle acd equals the measure of angle
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Question 920277: I do nit understand how to solve proofs. I have a proof that given triangle abc with exterior angle angle acd and the given is the measure of angle acd equals the measure of angle a plus the measure of angle b. I am totally lost on how to do it. Found 2 solutions by mananth, MathLover1:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! In triangle ABC
A + B +C = 180 degrees ( sum of angles of a triangle)
Angle ACB + Angle ACD = 180 degrees ( Linear angle)
Therefore
A + B +C = angle ACB + Angle ACD
Angle C is common
So A+B = angle ACD
You can put this solution on YOUR website!
Theorem: The measure of an exterior angle of a triangle equals the sum of the measures of the two interior, opposite (remote) angles.
given triangle abc with exterior angle angle acd and the given is the measure of angle acd equals the measure of angle a plus the measure of angle b
Proof:
statement:.................................................reason:
1) ∆ has exterior angle < ........- Given
2) < and < are the opposite interior
angles with respect to <.................- Definition of opposite interior angle
3) m< = °......................- Definition of straight angle
4) m< + < = m<..............- Angle addition postulate
5) m< + m< = °...........- Substitution (3) into (4)
6) m< + m< + m< = °........- Sum of interior angles of a triangle
7) m< + m<=m<+m<+m<.........Substitution (5) into (6)
8) m< = m< + m<............- Subtraction property of equality
