Question

statements reasons 1. ∠1 and ∠3 are complementary a. 2. b. definition of complementary angles 3. m∠abc = 90° c. definition of right angles 4. m∠abc = m∠1 + m∠2 d. 5. 90° = m∠1 + m∠2 e. substitution 6. ∠1 and ∠2 are complements f. 7. ∠2 is congruent to ∠3 g. m∠1 + m∠2 = 90° none of the answers m∠2 + m∠3 = 90° m∠1 + m∠3 = 90°

Explanation:

Step1: Given information

$\angle1$ and $\angle3$ are complementary, so $m\angle1 + m\angle3=90^{\circ}$ (by the definition of complementary angles).

Step2: Analyze angle - sum property

We know that $m\angle ABC = 90^{\circ}$ (by the definition of right - angles) and $m\angle ABC=m\angle1 + m\angle2$. So, by substitution, $90^{\circ}=m\angle1 + m\angle2$.

Step3: Use the property of complementary angles

Since $m\angle1 + m\angle3 = 90^{\circ}$ and $m\angle1 + m\angle2=90^{\circ}$, we can conclude that $\angle2\cong\angle3$ (by the congruence of angles that are complements of the same angle).

Step4: Check the options

The equation $m\angle1 + m\angle3 = 90^{\circ}$ is given by the definition of complementary angles for $\angle1$ and $\angle3$.

Answer:

$m\angle1 + m\angle3 = 90^{\circ}$