Question

if α = 119° and β = 30°, find γ in the following triangle. α + β + γ = 180° γ =

Explanation:

Step1: Recall angle - sum property

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

Step2: Rearrange the formula to solve for $\gamma$

$\gamma=180^{\circ}-\alpha - \beta$.

Step3: Substitute given values

Given $\alpha = 119^{\circ}$ and $\beta = 30^{\circ}$, then $\gamma=180^{\circ}-119^{\circ}-30^{\circ}$.

Step4: Calculate the value of $\gamma$

$\gamma = 31^{\circ}$.

Answer:

$31^{\circ}$