Bill knows that one angle in an isosceles triangle measures 100 degrees. If the other 2 angles are congruent, what is the measure of each of those angles?
Responses
A 40 degrees40 degrees
B 80 degrees80 degrees
C 60 degrees60 degrees
D 100 degrees
The sum of the angles in any triangle is 180 degrees. In an isosceles triangle, two angles are congruent. Let x be the measure of each of the congruent angles. Then we can set up the equation:
100 + x + x = 180
Simplifying and solving for x:
2x + 100 = 180
2x = 80
x = 40
Therefore, each of the congruent angles measures 40 degrees. Answer: A) 40 degrees.
In an isosceles triangle, the base angles (the angles opposite the congruent sides) are congruent. Since one angle in the triangle is known to measure 100 degrees, and the other two angles are congruent, the measure of each of those angles can be found by subtracting the known angle from 180 degrees (the sum of the interior angles of a triangle) and then dividing the result by 2.
Step 1: Subtract the known angle from 180 degrees: 180 - 100 = 80 degrees.
Step 2: Divide the result by 2 to find the measure of each of the congruent angles: 80 / 2 = 40 degrees.
Therefore, the measure of each of the congruent angles in the triangle is 40 degrees.
So, the correct answer is A) 40 degrees.