The acute angles of a right-angled triangle are 2: 7. What are these angles equal to?

Let’s denote by x half the size of the smaller of the acute angles of the given right-angled triangle.

Then the value of the smaller of the acute angles of the given right-angled triangle should be equal to 2x.

According to the condition of the problem, the acute angles of a right-angled triangle are 2: 7, therefore, the value of the largest of the acute angles of this right-angled triangle should be equal to 7x.

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

2x + 7x + 90 = 180,

solving which, we get:

9x + 90 = 180;

9x = 180 – 90;

9x = 90;

x = 90/9 = 10.

Find sharp corners:

2 * 10 = 20 °;

7 * 10 = 70 °.

Answer: 20 ° and 70 °.