Answer:
x = 25
y = 14
Explanation:
The described scenario can be represented using the attached triangle.
1- getting the value of x:
We know that ΔABC is an isosceles triangle with AC = BC
This means that:
∠CAB = ∠CBA
We know that ∠CAB = 50° and ∠CBA = 2x°
Equating the two angles, we get:
50 = 2x .................> Divide both sides by 2
x = 25
2- getting the value of y:
We know that the sum of the internal angles of a triangle is 180°
This means that:
∠ABC + ∠CAB + ∠ACB = 180°
We have:
∠ABC = 2x = 50°
∠ACB = 5y + 10
∠CAB = 50°
Now, we substitute to get the value of y as follows:
50 + 50 + 5y + 10 = 180
110 + 5y = 180
5y = 180 - 110
5y = 70 .............> Divide both sides by 5
y = 14
Hope this helps :)
