Question

in an isosceles triangle, the third angle is 10 times the measure of each of the congruent angles. What is the measure, in degrees, of the largest angle?

Answer 1

An isosceles triangle has two congruent angles and a third different angle.

Let's set x for each congruent angle.

Now, the third angle is 10 times the measure of each of the congruent angles.

Then:

Each congruent angle = x

The third angle = 10x

The sum of the measures of the interior angles of a triangle is 180 degrees.

Then:

x + x + 10x = 180

Solve for x:

12x = 180

Divide both sides by 12

12x/12 = 180/12

x = 15

Hence, each congruent angle has a measure of 15 degrees.

For the largest angle with a measure of 10x, we need to replace the x value:

10(15) =150

Therefore, the largest angle has a measure of 150 degrees.