The measure of an exterior angle of a triangle is 120. the interior angles that are not adjacent to this exterior angle are congruent. find the measures of the interior angles of the triangle
To find the measures of the interior angles of the triangle, we can use the fact that the sum of the measures of the three interior angles of any triangle is always 180 degrees.
Let's assume that the three interior angles that are congruent have a measure of x degrees. The measure of the exterior angle is given as 120 degrees.
Now, since the exterior angle and the interior angle adjacent to it on the triangle's side form a straight line, their measures add up to 180 degrees. Therefore, we can set up an equation:
x + 120 = 180
To solve for x, we isolate it by subtracting 120 from both sides of the equation:
x = 180 - 120
x = 60
So, the congruent interior angles of the triangle each have a measure of 60 degrees.