In an isosceles​ triangle, one angle is 66​° greater than each of the other two equal angles. Find the measure of all three angles.

Question

Find the two smaller angles

Find the larger angle

Answer 1

 I would've loved to draw a picture for you or import a picture, but I'll use words since I can't. We know an isosceles triangle has two equal angles, so lets call those angles x (that is, 2x). The other angle that's greater by 66° is 66 + x.

 

So, 66 + x + 2x = 180 => 3x = 180 - 66 = 114  => x = 114 / 3 = 38°

Answer 2

TWO EQUAL BASE ANGLES measure x^o each, and other (vertex angle) measures x+66 degrees.

 

Total is 180 so you can create an expression for the sum of the three angles, equate that to 180, and solve the resulting equation.