Complete the proof? ( Geometry) a question in my study guide

Complete the paragraph proof. Given <A and <B are complementary, and <B and<C are complementary. Prove <A = <C

By definition of complementary angles, m<A + blank =90 degrees and m<B+m<C= blank. Then, m<A+m<B=m<B+m<C by the blank. Subtract m<B from each side. You get blank = m<C or blank = <C

1 Answer
Nov 21, 2017

Please refer to Explanation.

Explanation:

By the Definition of Complementary Angles,

#m/_A+m/_B=90^@ and m/_B=m/_C=90^@....(1).#

Then, #m/_A+m/_B=m/_B+m/_C..........."[By, "(1)].#

Subtracting #m/_B# from each side,

#m/_A+m/_B-m/_B=m/_B+m/_C-m/_B.#

#:. m/_A+[m/_B-m/_B]=[m/_B-m/_B]+m/_C.#

#:. m/_A=m/_C.#

Hence, the Proof.