Question

current attempt in progress
if $alpha = 105^{circ}$ and $\beta = 48^{circ}$, find $gamma$ in the following triangle.
$alpha+\beta+gamma = 180^{circ}$

Explanation:

Step1: Recall angle - sum property of a triangle

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

Step2: Solve for $\gamma$

We can rewrite the equation as $\gamma=180^{\circ}-\alpha - \beta$. Substitute $\alpha = 105^{\circ}$ and $\beta = 48^{\circ}$ into the equation: $\gamma=180^{\circ}-105^{\circ}-48^{\circ}$.

Step3: Calculate $\gamma$

$\gamma = 27^{\circ}$.

Answer:

$27^{\circ}$