In triangle ABC, if AB = AC and angle A = 100 degrees, what is the measure of an

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Question: In triangle ABC, if AB = AC and angle A = 100 degrees, what is the measure of angles B and C?

Options:

Correct Answer: 40 degrees each

Solution:

In an isosceles triangle, angles B and C are equal. Therefore, angle B = angle C = (180 - 100) / 2 = 40 degrees.

In triangle ABC, if AB = AC and angle A = 100 degrees, what is the measure of angles B and C?

In triangle ABC, if AB = AC and angle A = 100 degrees, what is the measure of angles B and C?

Step 1: Identify that triangle ABC is isosceles because AB = AC.
Step 2: Recognize that in an isosceles triangle, the angles opposite the equal sides are also equal. This means angle B = angle C.
Step 3: Use the fact that the sum of all angles in a triangle is 180 degrees. Since angle A is 100 degrees, we can find the sum of angles B and C.
Step 4: Calculate the sum of angles B and C: 180 degrees - angle A = 180 - 100 = 80 degrees.
Step 5: Since angles B and C are equal, divide the sum of angles B and C by 2: 80 degrees / 2 = 40 degrees.
Step 6: Conclude that angle B = 40 degrees and angle C = 40 degrees.

Isosceles Triangle Properties – In an isosceles triangle, two sides are equal, which means the angles opposite those sides are also equal.
Triangle Sum Theorem – The sum of the interior angles of a triangle is always 180 degrees.