Question

Copy everything shown and supply missing statements and reasons.

Given: $\angle AOD$as shown

Prove: $m\angle AOD=m\angle 1+m\angle 2+m\angle 3$

Proof:

Short answer

From the given figure, it can be observed that $\angle AOC$and $\angle 3$are adjacent angles.

$m\angle AOD$can be written as the sum of two adjacent angles, that is, $m\angle AOC$and $m\angle 3$.

$m\angle AOD=m\angle AOC+m\angle 3$

Step-by-step solution

Step 1. Add adjacent angles.

From the given figure, it can be observed that $\angle AOC$and $\angle 3$are adjacent angles.

$m\angle AOD$can be written as the sum of two adjacent angles, that is, $m\angle AOC$and $m\angle 3$.

$m\angle AOD=m\angle AOC+m\angle 3$

Step 2. Add adjacent angles.

From the given figure, it can be observed that $\angle 1$and $\angle 2$are adjacent angles.

$m\angle AOC$can be written as the sum of two adjacent angles, that is, $m\angle 1$and $m\angle 2$.

$m\angle AOC=m\angle 1+m\angle 2$

Step 3. Apply substitution property of algebra.

Substitute$m\angle 1+m\angle 2$ for $m\angle AOC$into step 1.

$m\angle AOD=m\angle AOC+m\angle 3$

$=m\angle 1+m\angle 2+m\angle 3$

Hence it is proved that $m\angle AOD=m\angle 1+m\angle 2+m\angle 3$.