In an isosceles triangle, one angle is 63 degrees greater than each of the other two equal angles. Find the measure of all three angles.

Answer 1

This problem requires some background knowledge of isosceles triangles. First, in a triangle, the angles add to be 180 degrees. Second, isosceles means 2 of the angles are equal. So the third angle is the one described.

Let x be used as the base measure angle for the 2 angles that are equal. The third angle is then x + 63.

Now we set up the equation:

First angle + second angle + third angle = 180.

x + x + x+63 = 180.

3x + 63 = 180 Subtract 63 from both sides.

-63 -63

3x = 117 Divide 3 from both sides.

/3 /3

x = 39

So each of the 2 angles on the base are 39 degrees. The third angle is x + 63.

39 + 63 = 102

The 3 angles are 39, 39, and 102.

To check, add up the angle measures to see if they add to 180.

39 + 39 + 102 = 180!! Why, yes! Yes, it works.

I hope this helps.

Sue H.