A triangle is such that the largest angle is 11 times the smallest angle. The third angle is 27° less than the largest angle. Find the measure of each angle. (Enter solutions from smallest to largest.)

The largest angle = 11 * the smallest angle

The third angle = The largest angle - 27 ° = 11 * the smallest angle - 27 °

The angles of a triangle always sum to 180 °

The smallest angle + The largest angle + The third angle = 180 °

The smallest angle + 11 * the smallest angle + 11 * the smallest angle -27 ° = 180°

23 * the smallest angle - 27 ° = 180 °

23 * the smallest angle = 180 ° + 27 °

23 * the smallest angle = 207 ° Divide both sides by 23

The smallest angle = 207 ° / 23

The smallest angle = 9 °

The largest angle = 11 * the smallest angle

The largest angle = 11 * 9 °

The largest angle = 99 °

The third angle = The largest angle - 27 °

The third angle = 99 ° - 27 °

The third angle = 72 °

72 ° + 99 ° + 9 ° = 180 °

To solve this problem, we can set up a system of equations based on the given information.

Let's denote the smallest angle as x degrees.

According to the problem, the largest angle is 11 times the smallest angle, so the largest angle is 11x degrees.

The third angle is 27° less than the largest angle, so the third angle is (11x - 27) degrees.

Since the sum of angles in a triangle is always 180 degrees, we can write the equation:

x + 11x + (11x - 27) = 180

Simplifying the equation, we get:

23x - 27 = 180

Adding 27 to both sides of the equation, we get:

23x = 207

Dividing both sides of the equation by 23, we get:

x = 9

Now that we have found the value of x, we can substitute it back into the equations to find the measure of each angle.

The smallest angle is x = 9 degrees.

The largest angle is 11x = 11 * 9 = 99 degrees.

The third angle is (11x - 27) = (11 * 9 - 27) = 72 degrees.

Therefore, the measures of the angles in the triangle are 9 degrees, 72 degrees, and 99 degrees.