Question

1. complete the following proof: given: ∠abc is a right angle prove: ∠1 and ∠2 are complementary statements reasons ∠abc 1. given 2. definition of right angles 3. angle addition postulate ∠1 + ∠2 = 90° 4. 5.

Explanation:

Step1: State given information

$\angle ABC$ is a right - angle

Step2: Define right angle

$m\angle ABC = 90^{\circ}$ (by definition of right angles)

Step3: Apply angle - addition postulate

$m\angle1 + m\angle2=m\angle ABC$ (angle addition postulate)

Step4: Substitute the value of $\angle ABC$

$m\angle1 + m\angle2 = 90^{\circ}$ (substitution property of equality)

Step5: Define complementary angles

$\angle1$ and $\angle2$ are complementary (by definition of complementary angles: two angles are complementary if the sum of their measures is $90^{\circ}$)

Answer:

Statements	Reasons
2. $m\angle ABC = 90^{\circ}$	2. Definition of Right Angles
3. $m\angle1 + m\angle2=m\angle ABC$	3. Angle Addition Postulate
4. $m\angle1 + m\angle2 = 90^{\circ}$	4. Substitution Property of Equality
5. $\angle1$ and $\angle2$ are complementary	5. Definition of Complementary Angles