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.
