One of the angles of the triangle is 2 times larger than the second, and the third angle is 57

One of the angles of the triangle is 2 times larger than the second, and the third angle is 57 °. Find two unknown angles of a triangle

From the condition it is known that one of the angles of the triangle is 2 times larger than the second, and it is also known that the third angle is 57 °.

To solve the problem, we will compose and solve an equation. To do this, we apply the theorem on the sum of the angles of a triangle. It says that the sum of the angles of a triangle is 180 °.

We denote by x ° the smaller of the unknown angles of the triangle, then the degree measure of the second unknown angle is 2x °.

We get the equation:

x + 2x + 57 = 180;

3x = 180 – 57;

3x = 123;

x = 41 °, then 2 * 41 = 82 °.