Question

given: $angle 1$ is complementary to $angle 2$.$angle 2$ is complementary to $angle 3$.prove: $mangle 1 = mangle 3$what is the missing statement in step 3 of the proof?$\bigcirc$ $mangle 1 = mangle 2LXB0\bigcirc$ $mangle 2 = mangle 3$$\bigcirc$ $mangle 2 + mangle 3 = 180^circ$| statements | reasons || ---- | ---- || 1. $angle 1$ is comp. to $angle 2$ | 1. given || 2. $angle 2$ is comp. to $angle 3$ | 2. given || 3. ? | 3. def. of comp. $angle$s || 4. $mangle 1 = 90^circ - mangle 2$ | 4. subtr. equality prop. || 5. $mangle 2 + mangle 3 = 90^circ$ | 5. def. of comp. $angle$s || 6. $mangle 3 = 90^circ - mangle 2$ | 6. subtr. equality prop. || 7. $mangle 1 = mangle 3$ | 7. trans prop. |

Explanation:

Step1: Recall complementary angles def

Complementary angles sum to $90^\circ$.

Step2: Match reason to statement

Reason 3 is "def of comp. ∠s", so we use the definition for ∠1 and ∠2.

Step3: Identify correct statement

From given ∠1 complementary to ∠2, the definition gives $m\angle1 + m\angle2 = 90^\circ$.

Answer:

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