Question

big ideas math integrated - algebra 1 > proofs involving angles: justify a statement 222
∠x and ∠v are complementary and ∠w and ∠v are complementary. complete the proof that ∠w ≅ ∠x.

	statement	reason
2	∠w and ∠v are complementary	given
3	( mangle x + mangle v = 90^circ )
4	( mangle w + mangle v = 90^circ )	definition of complementary angles
5	( mangle x + mangle v = mangle w + mangle v )	transitive property of equality
6	( mangle w = mangle x )	properties of addition, subtraction, multiplication, and division
7	( angle w cong angle x )	definition of congruence

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Explanation:

Step1: Recall complementary angles definition

Complementary angles are two angles whose measures add up to \( 90^\circ \). Since \( \angle X \) and \( \angle V \) are complementary (from Statement 1), by the definition of complementary angles, we have \( m\angle X + m\angle V = 90^\circ \).

Answer:

Definition of complementary angles