The 60 degree angle is divided into two angles that are 2: 3. What is the degree measure of the larger of these two?

Let us denote by x the value of the larger of the two given angles into which the angle of 60 ° is divided, expressed in degrees.

According to the condition of the problem, the values of these angles relate to each other as 2: 3, therefore, the value of the smaller angle is (2/3) x.

Since these two angles add up to an angle of 60 °, we can write the following equation:

x + (2/3) x = 60.

We solve the resulting equation and find a larger angle:

(3/3) x + (2/3) x = 60;

(5/3) x = 60;

x = 60 / (5/3);

x = 60 * 3/5;

x = 36 °.

Answer: The larger angle is 36 °.