△ABC
is an isosceles triangle. <B is the vertex angle. What is the measure of <C if the m<B = 90 degrees?(1 point)
Responses
45 degrees
90 degrees
15 degrees
30 degrees
Since triangle ABC is isosceles, it means that angles A and C are equal.
We also know that angle B is 90 degrees.
Since the sum of angles in a triangle is 180 degrees, we can find the measure of angle C by subtracting the sum of angles A and B from 180 degrees.
Angle A + Angle B + Angle C = 180 degrees
Angle A + 90 degrees + Angle C = 180 degrees
Since Angle A and Angle C are equal, we can replace Angle A with Angle C:
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 is 45 degrees.