Question

write a justification for each step, given that m∠1 + m∠2 = 90° and m∠2 + m∠3 = 90°. 1. m∠1 + m∠2 = 90° m∠2 + m∠3 = 90° 2. m∠1 + m∠2 = m∠2 + m∠3 3. m∠1 = m∠3 1. given 2. def. of comp. ∠s 3. subtr. prop. of = 1. given 2. sym. prop. of = 3. add. prop. of = 1. given 2. trans. prop. of = 3. subtr. prop. of = 1. given 2. def. of supp. ∠s 3. add. prop. of =

Explanation:

Step1: Justify initial statements

Given $m\angle1 + m\angle2 = 90^\circ$ and $m\angle2 + m\angle3 = 90^\circ$.

Step2: Set equal via transitivity

By Transitive Property of Equality, $m\angle1 + m\angle2 = m\angle2 + m\angle3$.

Step3: Subtract common angle

Using Subtraction Property of Equality, subtract $m\angle2$ from both sides: $m\angle1 = m\angle3$.

Answer:

1. Given, 2. Trans. Prop. of =, 3. Subtr. Prop. of =