a. Transitive Property: This property states that if a = b and b = c, then a = c. In this case, <2 = <4 and m<2 = m<4, so <2 = m<4.
b. Definition of Supplementary Angles: Supplementary angles are two angles whose measures add up to 180 degrees. Since <3 and <4 are a linear pair, they are supplementary angles.
c. Subtraction Property of Equality: This property states that if a = b, then a - c = b - c. In this case, m<3 + m<4 = 180, so m<3 + 110 = 180, so m<3 = 70.
Given: <2 = <4, m<2 = 110
Proof: m<3 = 70
<2 = <4, m<2 = 110 Given
m<2 = m<4 Definition of congruent angles
m<4 = 110 b._______
<3 and <4 are a linear pair Definition of a linear pair(shown in diagram)
<3 and <4 are supplementary Linear Pair postulate
m<3 + m<4 = 180 c.________
m<3 = 70 d._______
I know the answers are a. Transitive
b. Definition of supplementary angles
c. Subtraction property of equality
but why? explain please!!
1 answer