△ABC is an isosceles triangle. <B is the vertex angle. What is the measure of <C if the m<B = 90 degrees?
30 degrees
15 degrees
90 degrees
45 degrees
Since triangle ABC is isosceles, it has two congruent angles. Therefore, angle A and angle C are congruent.
Since angle B is 90 degrees, the sum of the angles in a triangle is 180 degrees, we can conclude:
angle A + angle B + angle C = 180 degrees.
Since angle A = angle C, we can rewrite the equation:
angle C + 90 degrees + angle C = 180 degrees.
Combining like terms:
2*angle C + 90 degrees = 180 degrees.
Subtracting 90 degrees from both sides:
2*angle C = 90 degrees.
Dividing both sides by 2:
angle C = 45 degrees.
Therefore, the measure of angle C in triangle ABC is 45 degrees.