Academic Team – Math Practice Test

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In triangle ABC, if side AB is congruent to side BC and angle A measures 47°, what is the measure of angle B?

47°

86°

In triangle ABC, since side AB is congruent to side BC, triangle ABC is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, angles A and B are congruent because they are opposite the equal sides AB and BC, respectively.

Given that angle A measures 47°, it follows that angle B must also measure 47° since they are opposite the congruent sides. To find the measure of angle C, we can use the fact that the sum of all interior angles in a triangle is always 180°.

So, we set up the equation for the sum of angles:

Angle A + Angle B + Angle C = 180°

Substituting the values we know:

47° + 47° + Angle C = 180°

This simplifies to:

94° + Angle C = 180°

To find Angle C, we subtract 94° from 180°:

Angle C = 180° - 94° = 86°

Thus, the measure of angle B, which we initially identified as being the same as angle A, confirms that angle B measures 47°. It’s evident that the measure of angle C, which is

43°

90°