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question 12 of 22
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consider the triangle shown in the figure below. if $alpha = 107.5^{circ}$ and $gamma = 14.4^{circ}$, find $\beta$.
$alpha+\beta+gamma = 180^{circ}$
enter the exact answer.
$\beta=$

Explanation:

Step1: Recall angle - sum property

The sum of angles in a triangle is 180°, so $\alpha+\beta+\gamma = 180^{\circ}$.

Step2: Solve for $\beta$

We can rewrite the formula as $\beta=180^{\circ}-\alpha - \gamma$.
Substitute $\alpha = 107.5^{\circ}$ and $\gamma = 14.4^{\circ}$ into the formula: $\beta=180^{\circ}-107.5^{\circ}-14.4^{\circ}$.
First, $180^{\circ}-107.5^{\circ}=72.5^{\circ}$.
Then, $72.5^{\circ}-14.4^{\circ}=58.1^{\circ}$.

Answer:

$58.1^{\circ}$