The diagonal AC is drawn in the rectangle ABCD. It is known that the angle BAC is 2 times greater than

The diagonal AC is drawn in the rectangle ABCD. It is known that the angle BAC is 2 times greater than the angle ACB. What are these angles

A rectangle is a quadrilateral in which all corners are straight, and opposite sides are parallel and equal to each other.

In order to find the degree measures of the angles ∠ACB and ∠BAC, consider the triangle ΔABS. This triangle is right-angled with a right angle ∠B.

Since the sum of all the angles of the triangle is 180º, and the angle BAC is twice the angle ∠ACB, then:

x is the degree measure of the angle ∠АСВ;

2x – the degree measure of the angle ∠BAC;

90º – the value of the angle ∠АВС;

180º – the sum of all the angles of the triangle4

x + 2x + 90 = 180;

x + 2x = 180 – 90;

3x = 90;

x = 90/3 = 30;

∠АСВ = 30º;

∠ВАС = 30 ∙ 2 = 60º.

Answer: the degree measure of the angle ∠АСВ is equal to 30º; the angle ∠BAC is equal to 60º.