Answers:
- α = 62 degrees
- β = 100 degrees
- γ = 78 degrees
Step-by-step explanation
The first three lowercase letters of the Greek alphabet are α, β, γ. They have the names alpha, beta, and gamma in that order.
The triangle on the left side has angles 56, alpha, and alpha. It's not a typo that alpha is listed twice. This is because the isosceles triangle has congruent base angles. The base angles are opposite the congruent sides (shown with tickmarks).
Let's find alpha.
We'll use the fact that the inside angles of a triangle add to 180.
56 + α + α = 180
2α + 56 = 180
2α = 180-56
2α = 124
α = 124/2
α = 62 degrees
Now focus on the triangle on the right side. It has angles of beta up top, and two copies of 40 degrees for each base angle down below.
Let's find beta.
40+β+40 = 180
β + 80 = 180
β = 180-80
β = 100 degrees
The last variable we need is gamma. This angle is between the two triangles. Notice that the other angles next to gamma are alpha = 62 and the 40 degree angle I mentioned earlier. This is the other base angle.
These three angles are supplementary since they form a straight line. The angles add to 180 degrees.
α + γ + 40 = 180
62 + γ + 40 = 180
γ + 102 = 180
γ = 180-102
γ = 78 degrees