Question

given: ∠1 is complementary to ∠2. ∠2 is complementary to ∠3. prove: m∠1 = m∠3. what is the missing statement in step 3 of the proof? statements: 1. ∠1 is comp. to ∠2 2. ∠2 is comp. to ∠3 3.? 4. m∠1 = 90° - m∠2 5. m∠2 + m∠3 = 90° 6. m∠3 = 90° - m∠2 7. m∠1 = m∠3 reasons: 1. given 2. given 3. def. of comp. ∠s 4. subtr. equality prop 5. def. of comp. ∠s 6. subtr. equality prop 7. trans. prop.

Explanation:

Step1: Recall definition of complementary angles

If two angles are complementary, the sum of their measures is 90 degrees. Since $\angle1$ is complementary to $\angle2$, we have $m\angle1 + m\angle2=90^{\circ}$. Since $\angle2$ is complementary to $\angle3$, we have $m\angle2 + m\angle3 = 90^{\circ}$. The missing step 3 uses the definition of complementary - angles.

Step2: Identify the correct statement

The correct statement for step 3 based on the definition of complementary angles is $m\angle1 + m\angle2 = 90^{\circ}$.

Answer:

$m\angle1 + m\angle2 = 90^{\circ}$