Question

In an isosceles triangle, one angle is 33 degrees greater than each of the other two equal angles. Find the measure of all three angles

Answer 1

in an isosceles triangle, the angles opposite of the apex are equal. The three angles in any triangle equal 180 degrees. Now, if we let x represent one of the angles opposite the apex, then the angel at the apex will be

`x\text{ + 33}`

Adding up the three angles will equal 180:

`x\text{ + x + (x+33) = 180}`

this is equivalent to:

`3x\text{ = 180-33 = 147}`

that is:

`3x\text{ = 147}`

solving for x, we get:

`x\text{ = }(147)/(3)\text{ = 49}`

We can conclude that the angles in the isosceles triangle are 49 degrees, 49 degrees, and (x+33)= (49+33) = 82 degrees. Then, the correct answer is:

Angle 1: 49 degrees

Angle 2: 49 degrees

Angle 3: 82 degrees