Question

what is the reason for statement 7 of the two-column proof? ruler postulate
linear pair postulate
angle addition postulate
angle congruence postulate
given: ∠a and ∠b are supplementary. m∠a=90° prove: ∠a≅∠b statements reasons
1. ∠a and ∠b are supplementary. given 2. m∠a+m∠b=180° definition of supplementary angles
3. m∠a=90° given
4. 90°+m∠b=180° substitution property of equality
5. m∠b=90° subtraction property of equality
6. m∠a=m∠b substitution property of equality
7. ∠a≅∠b

Answer 1

Answer: Angle congruence postulate is the right answer.

Angle congruence postulate tells that if measurement of two angles are equal then they are congruent or same.

Given: ∠a and ∠b are supplementary and m∠a=90°.

as  ∠a and ∠b then  ∠a + ∠b = 180° (by definition of supplementary angles)

⇒90°+∠b=180°......(by putting given value of ∠a=90°)

⇒∠b=90.........(by adding -90 on the both sides)

⇒m∠a=m∠b (substitution property of equality)  

⇒ ∠a≅∠b (by angle congruence postulate)