Question

What is the value for y?

Answer 1

If the two sides of the triangle are equal (or two angles), it is an isosceles triangle. An isosceles triangle has two equal sides and two equal angles. So that means that 50 degrees equals 2x, so 2x is 50 degrees. The sum of angles in a triangle is 180 degrees, so to find 5y + 10, you do 180 - 50 - 50 = 80 degrees. So 5y + 10 = 80 degrees, and here you can solve.

5y + 10 = 80

5y = 80 - 10

5y = 70

y = 70/5

y = 14

Answer 2

This is an isosceles triangle. The angles at the base have equal measures.

Therefore we have:

$2x=50$    divide both sides by 2

$x=25$

We know that the sum of the measures of the angles in a triangle is 180°.

Therefore we have the equation:

$50^o+2x^o+(5y+10)^o=180^o\\\\50+50+5y+10=180$

$110+5y=180$     subtract 110 from both sides

$5y=70$      divide both sides by 5

$\boxed{y=14}$