In triangle ABC, angle A is 4 times less than angle B, and at head C it is 90 degrees less than angle B.

In triangle ABC, angle A is 4 times less than angle B, and at head C it is 90 degrees less than angle B. a) find the angles of the triangle. b) compare sides AB and BC

Let the value of the angle BAC be equal to X0, then, according to the condition, the angle ABC = 4 * X0, and the angle ACB = (4 * X – 90) 0.

The sum of the interior angles of a triangle is 180, then:

180 = (X + 4 * X + (4 * X – 90)) = 9 * X – 90.

9 * X = 180 + 90 = 270.

X = 270/9 = 30.

Angle BAC = X0 = 30, angle ABC = 4 * X = 4 * 30 = 120, angle ACB = (120 – 90) – 30.

Since the angle BAC = BAC, the triangle ABC is isosceles, and therefore AB = BC.

Answer: The angles of the triangle ABC are equal to 30, 30, 120. The segments AB and BC are equal.