In an isosceles triangle, one angle is 45 degrees greater than each of the other two equal angles. Find the measure of all three angles.

Question

 In an isosceles triangle, one angle is 45 degrees greater than each of the other two equal angles. Find the measure of all three angles.

Answer 1

Let x = the measure of one of the two equal base angles; then the other angle mentioned must be x + 45.

Therefore the total is x + x +(x+45) = 180 or 3x = 135.

 

x = 45^oso the triangle is 45-45-90!

Answer 2

Hi Courtney, in an isosceles triangle, the angles opposite of the apex are equal. The three angles in any triangle equals 180 degrees.

 

If we let x represent one of the angles opposite the apex, then the angel at the apex will be x + 45.

 

Adding up the three angles will equal 180.

 

x + x + (x + 45) = 180

 

Clear the parentheses:

 

3x + 45 = 180

 

Subtract 45 from both sides:

 

3x = 135

 

Divide both sides by 3:

 

x = 45

 

The angles in the isosceles triangle are 45 degrees, 45 degrees, and 90 degrees.

 

Questions?