This Is A World Problem

Question

One angle in an isosceles triangle is six times as large as the two congrurnt angles in the triangle. What is the measure of each angle in the triangle?

Answer 1

The sum of the angles in any triangle is always 180^o. Therefore, if we say that the two congruent angles in the triangle each measure "x" degrees, we can set up an equation as follows:

x + x + 6x = 180; 8x = 180; x = 22.5

Therefore, the angles in this triangle measure 22.5^o, 22.5^o, and 135^o.

I hope this helped!

Answer 2

For a triangle the 3 angles add up to be 180°

Since it's an isosceles triangle two angles are the same.

It states that the larger angle is 6 times the congruent angle.

Let x= the congruent angle

x+x+6x=180°

8x=180°

x=22.5°

6(22.5°)=135°

Check to verify that it adds up to 180°

22.5+22.5+135=180 <--- YES it adds up

So the two congruent angles are 22.5° and the larger angle is 135°

Answer 3

Let "x" be the measure of the "one angle". Then the two congruent angles are 1/6x.

Since there are 180° in a triangle, then x + 1/6x + 1/6x = 180

x + 1/6x + 1/6x = 180

6/6x + 1/6x + 1/6x = 180

8/6x = 180

x = 180(6/8) = 135

1/6x = 22.5

So the "one angle" is 135° and the two congruent angles are 22.5°