Angle A = 45 degrees of triangle ABC, and angle C is 4 times greater than angle B, find the degree measure

Angle A = 45 degrees of triangle ABC, and angle C is 4 times greater than angle B, find the degree measure of angles B and C.

Find the angles of the triangle ABC if ∠ A = 45 °.
Let ∠ B = x.
Since ∠C is 4 times more than ∠B, then ∠C = 4 * ∠ A = 4 * x.
The sum of all the angles of a triangle is 180 °.
∠ A + ∠ B + ∠ C = 180 °;
45 ° + x + 4 * x = 180 °;
45 ° + 5 * x = 180 °;
5 * x = 180 ° – 45 °;
5 * x = 135 °;
x = 135 ° / 5;
x = 27 °;
Hence, ∠ B = 27 °;
Find ∠ С.
∠ C = 4 * x = 4 * 27 ° = 108 °.
Answer: ∠ В = 27 ° and ∠ С = 108 °.