In triangle ABC, if AB = AC and angle A = 40 degrees, what are the measures of a

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Question: In triangle ABC, if AB = AC and angle A = 40 degrees, what are the measures of angles B and C?

Options:

Correct Answer: 80 degrees each

Solution:

Since AB = AC, angles B and C are equal. Therefore, angle B + angle C = 140 degrees, and each angle is 70 degrees.

In triangle ABC, if AB = AC and angle A = 40 degrees, what are the measures of angles B and C?

In triangle ABC, if AB = AC and angle A = 40 degrees, what are the measures of angles B and C?

Step 1: Identify that triangle ABC is an isosceles triangle because AB = AC.
Step 2: Recognize that in an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, 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 (which is 40 degrees) into the equation: 40 degrees + angle B + angle C = 180 degrees.
Step 5: Since angle B = angle C, we can write it as 40 degrees + 2 * angle B = 180 degrees.
Step 6: Simplify the equation: 2 * angle B = 180 degrees - 40 degrees, which is 140 degrees.
Step 7: Divide both sides by 2 to find angle B: angle B = 140 degrees / 2 = 70 degrees.
Step 8: Since angle B = angle C, angle C is also 70 degrees.

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