Which of the following angles in triangle ABC can be determined if side AB is equal to side BC?

Which of the following angles in triangle ABC can be determined if side AB is equal to side BC?

• A. Angle A
• B. Angle B
• C. Angle C
• D. None

Answer: (B)

In triangle ABC, if side AB is equal to side BC, the triangle is classified as isosceles. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, since AB is equal to BC, the angles opposite these sides, which are angle A and angle C, will be equal. However, the question asks specifically which angle can be determined. Knowing that angle B is included between the two equal sides (AB and BC), it can be calculated by using the properties of the triangle. We can use the triangle sum theorem, which states that the sum of the angles in any triangle is always 180 degrees. If we know the measures of the two equal angles (A and C), we can easily determine angle B. For example, if the two equal angles (let's say A and C) are known or can be deduced from other information, then angle B can be solved as follows: Angle B = 180° - (Angle A + Angle C) This direct relationship allows us to determine angle B once A and C are established. Thus, the conclusion is that angle B is the angle that can be determined based on the property of isosceles triangles.

In triangle ABC, if side AB is equal to side BC, the triangle is classified as isosceles. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, since AB is equal to BC, the angles opposite these sides, which are angle A and angle C, will be equal.

However, the question asks specifically which angle can be determined. Knowing that angle B is included between the two equal sides (AB and BC), it can be calculated by using the properties of the triangle. We can use the triangle sum theorem, which states that the sum of the angles in any triangle is always 180 degrees. If we know the measures of the two equal angles (A and C), we can easily determine angle B.

For example, if the two equal angles (let's say A and C) are known or can be deduced from other information, then angle B can be solved as follows:

Angle B = 180° - (Angle A + Angle C)

This direct relationship allows us to determine angle B once A and C are established. Thus, the conclusion is that angle B is the angle that can be determined based on the property of isosceles triangles.