Find the three angles of the triangle if you know that the second angle is twice the first

Find the three angles of the triangle if you know that the second angle is twice the first and the third is 60 degrees greater than the first.

Let us denote the angles of the triangle as <A, <B, and <C, and write down all the equalities according to the condition: <B = 2 * (<A), <C = <A + 60 °. But the main condition is: the sum of the angles <A + <B + <C = 180 °.

In the last equality we insert all the values of the angles through <A, then it turns out: <A + 2 * (<A) + (<A + 60 °) = 4 * (<A) + 60 ° = 180 °. From where: (<A) = (180 ° – 60 °) / 3 = 120 ° / 4 = 30 °. Determine the remaining angles of the triangle: <B = 2 * (<A) = 2 * 30 ° = 60 °. <C = <A + 60 ° = 30 ° + 60 ° = 90 °.

Check: <A + <B + <C = 30 ° + 60 ° + 90 ° = 180 °.