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In triangle ABC, if AB = AC and angle A = 40°, what is the measure of angle B?

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

Options:

  1. 40°
  2. 70°
  3. 80°
  4. 60°

Correct Answer: 70°

Solution: 

In an isosceles triangle, the base angles are equal. Therefore, angle B = angle C. Since the sum of angles in a triangle is 180°, we have 40° + 2B = 180°, leading to B = 70°.

In triangle ABC, if AB = AC and angle A = 40°, what is the measure of angle B?

Practice Questions

Q1
In triangle ABC, if AB = AC and angle A = 40°, what is the measure of angle B?
  1. 40°
  2. 70°
  3. 80°
  4. 60°

Questions & Step-by-Step Solutions

In triangle ABC, if AB = AC and angle A = 40°, what is the measure of angle B?
  • 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: Write down the known angle, which is angle A = 40°.
  • Step 4: Use the fact that the sum of all angles in a triangle is 180°. So, we can write the equation: angle A + angle B + angle C = 180°.
  • Step 5: Substitute the known values into the equation: 40° + angle B + angle B = 180°.
  • Step 6: Simplify the equation: 40° + 2 * angle B = 180°.
  • Step 7: Subtract 40° from both sides: 2 * angle B = 180° - 40°.
  • Step 8: Calculate the right side: 2 * angle B = 140°.
  • Step 9: Divide both sides by 2 to find angle B: angle B = 140° / 2.
  • Step 10: Calculate the final value: angle B = 70°.
  • Isosceles Triangle Properties – In an isosceles triangle, the angles opposite the equal sides are equal.
  • Triangle Angle Sum Theorem – The sum of the interior angles of a triangle is always 180°.
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