One corner of the triangle is 15 degrees smaller from the other and 5 times larger

One corner of the triangle is 15 degrees smaller from the other and 5 times larger beyond the third corner. Determine the type of triangle

The sum of all angles in a triangle is always 180 ° (according to the property of triangles). Let’s solve the problem using the equation, where:

x ° is the first corner of the triangle;

Then:

(x + 15) ° – the second corner of the triangle (since it is 15 ° more than the first);

x / 5 ° is the third corner of the triangle (since it is 5 times smaller than the first).

Let’s compose and solve the equation:

x + x + 15 + x / 5 = 180;

2x + x / 5 = 180 – 15;

2x + x / 5 = 165;

10x / 5 + x / 5 = 165 (brought to a common denominator);

11x / 5 = 165;

11x = 165 * 5;

11x = 825;

x = 825/11;

x = 75 ° – the first angle;

x + 15 = 75 + 15 = 90 ° – the second angle;

x / 5 = 75/5 = 15 ° is the third angle.

The triangle is rectangular.

Answer: 90 °; 75 °; 15 °