Question

In Example 3, find $m\angle 2,m\angle 3,m\angle 4,$ and $m\angle 5$.

Short answer

The measures of the all angles are: $m\angle 2=46°$, $m\angle 3=56°$, $m\angle 4=91°$ and $m\angle 5=74°$.

Step-by-step solution

Step 1. Given Information.

The figure is shown below.

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Step 2. Formula used.

$\text{Exterior angle}=180{}^{\circ }-\text{Interior angle}$

Step 3. Calculation.

Subtract $134°$ from $180°$ to calculate $m\angle 2$.

$\begin{array}{c}m\angle 2=180°-134°\\ m\angle 2=46°\end{array}$

Subtract $124°$ from $180°$ to calculate $m\angle 3$.

$\begin{array}{l}m\angle 3=180°-124°\\ m\angle 3=56°\end{array}$

Subtract $89°$ from $180°$ to calculate $m\angle 4$.

$\begin{array}{l}m\angle 4=180°-89°\\ m\angle 4=91°\end{array}$

Subtract $106°$ from $180°$ to calculate $m\angle 5$.

$\begin{array}{l}m\angle 5=180°-106°\\ m\angle 5=74°\end{array}$

Step 4. Conclusion.

The measures of all the angles are $m\angle 2=46°$,$m\angle 3=56°$,$m\angle 4=91°$ and $m\angle 5=74°$.