Question

question 11 of 22 if γ = β and α = 3β, find all three angles in the following triangle. α + β + γ = 180° α = β = γ =

Explanation:

Step1: Substitute angle - relationships into sum - of - angles formula

Since $\gamma=\beta$ and $\alpha = 3\beta$, and $\alpha+\beta+\gamma=180^{\circ}$, we substitute to get $3\beta+\beta+\beta = 180^{\circ}$.

Step2: Combine like - terms

Combining the terms on the left - hand side, we have $5\beta=180^{\circ}$.

Step3: Solve for $\beta$

Dividing both sides by 5, we get $\beta=\frac{180^{\circ}}{5}=36^{\circ}$.

Step4: Find $\alpha$ and $\gamma$

Since $\gamma=\beta$, then $\gamma = 36^{\circ}$. Since $\alpha = 3\beta$, then $\alpha=3\times36^{\circ}=108^{\circ}$.

Answer:

$\alpha = 108^{\circ}$
$\beta = 36^{\circ}$
$\gamma = 36^{\circ}$