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