Question

$\angle 1$ and $\angle 2$ are given. You see two attempts at constructing an angle whose measure is equal to $m\angle 1+m\angle 2.$ Are both constructions satisfactory$?$

Short answer

Yes,the construction is satisfactory.

Step-by-step solution

Step 1. Given information.

The figures here given are,

Step 2. Consider the first construction.

First $\angle 1$ is constructed and then $\angle 2$ is constructed.

Then one can say,

$m\angle SAY=m\angle 1+m\angle 2$.

The construction is satisfactory.

Step 3. Consider the second construction.

Here also first $\angle 1$ is constructed and then $\angle 2$.

Then one can say,

$m\angle OUI=m\angle 1+m\angle 2$.

The construction is satisfactory.

Therefore, we can say that both the constructions are satisfactory.