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

| February 15, 2021 | education

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

Let’s denote the value of the angle ACB through x.

Let us express the value of the angle BAC in terms of x.

According to the condition of the problem, the value of the angle BAC is 2 times greater than the value of the angle ACB, therefore, the value of the angle BAC is 2x.

Consider a triangle ABC.

In this triangle, the angle ABC is right.

Since the sum of the angles of any triangle is 180 °, we can write the following equation:

x + 2x + 90 = 180.

We solve the resulting equation and find the value of the angle ACB:

3x + 90 = 180;

3x = 180 – 90;

3x = 90;

x = 90/3;

x = 30 °.

We find the value of the angle BAC:

2x = 2 * 30 = 60 °.

Answer: ACB angle is 30 °, BAC angle is 60 °.



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