Triangle KLM set. The angle K is 2 times less than the angle L, and the angle M is more than the angle

Triangle KLM set. The angle K is 2 times less than the angle L, and the angle M is more than the angle L by 30 °. Find all the corners of the triangle. Which side is larger than KL or LM?

Given:

triangle KLM,

angle L = 2 * angle K degrees,

angle M = angle L + 30 degrees.

Find the degree measures of the angles of the triangle KLM, that is, angle K, angle M, angle L and determine which side is greater than KL or LM?

Solution:

Let the degree measure of the angle K be x degrees, then the degree measure of the angle L is 2 * x degrees, and the degree measure of the angle M is 2 * x + 30 degrees. We know that the sum of the degree measures of the angles of a triangle is 180 degrees. Let’s make the equation:

x + 2 * x + 2 * x + 30 = 180;

x + 2 * x + 2 * x = 180 – 30;

5 * x = 150;

x = 150: 5;

x = 30 degrees – angle K;

2 * 30 = 60 degrees – angle L;

60 + 30 = 90 degrees – angle M.

Opposite the larger corner is the larger side. Then the side KL, since it lies opposite a 90 degree angle.

Answer: 30 degrees; 60 degrees; 90 degrees; KL is greater than LM.