In triangle ABC, if AB = AC and angle A = 40 degrees, what is the measure of ang

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Question: In triangle ABC, if AB = AC and angle A = 40 degrees, what is the measure of angle B? (2023)

Options:

Correct Answer: 80 degrees

Exam Year: 2023

Solution:

In an isosceles triangle, angles opposite to equal sides are equal. Therefore, angle B = angle C = (180 - 40) / 2 = 70 degrees.

In triangle ABC, if AB = AC and angle A = 40 degrees, what is the measure of angle B? (2023)

In triangle ABC, if AB = AC and angle A = 40 degrees, what is the measure of angle B? (2023)

Step 1: Identify that triangle ABC is isosceles because AB = AC.
Step 2: Recall that in an isosceles triangle, the angles opposite the equal sides are equal. This means angle B = angle C.
Step 3: Use the fact that the sum of all angles in a triangle is 180 degrees. So, angle A + angle B + angle C = 180 degrees.
Step 4: Substitute the known value of angle A into the equation: 40 + angle B + angle B = 180.
Step 5: Simplify the equation: 40 + 2 * angle B = 180.
Step 6: Subtract 40 from both sides: 2 * angle B = 140.
Step 7: Divide both sides by 2 to find angle B: angle B = 70 degrees.

Isosceles Triangle Properties – In an isosceles triangle, the angles opposite the equal sides are equal, and the sum of the angles in any triangle is 180 degrees.
Angle Sum Property – The sum of the interior angles of a triangle is always 180 degrees.