In triangle ABC, line AB is congruent to line BC. If m angle A is 45, find m angle B.
90
Wouldn't it be 45, since it's an isosceles triangle?
...B...
A.....C
Angle A = Angle C, since AB is congruent to BC
Oops, it says angle B, not C.
Sorry.
To determine the measure of angle B, we can use the fact that the sum of the angles in a triangle is always 180 degrees. In this case, since angle A is given as 45 degrees, we can proceed as follows:
1. Triangle ABC has two congruent sides, AB and BC. This implies that angle A is congruent to angle C because these angles are opposite the congruent sides.
2. Since the sum of angle measures in a triangle is 180 degrees, the sum of angles A, B, and C must be 180 degrees.
3. We know that angle A is 45 degrees and angle C is congruent to angle A, so angle C is also 45 degrees.
4. Now, we can find the measure of angle B. By subtracting the sum of angles A and C (45 + 45 = 90 degrees) from the total sum of angles in a triangle (180 degrees), we can find angle B.
Angle B = 180 degrees - (angle A + angle C)
Angle B = 180 degrees - (45 degrees + 45 degrees)
Angle B = 180 degrees - 90 degrees
Angle B = 90 degrees
Therefore, the measure of angle B in triangle ABC is 90 degrees.