In the unfolded angle ABC, the beam BD is drawn so that it divides the unfolded

In the unfolded angle ABC, the beam BD is drawn so that it divides the unfolded angle into two angles, the degree measures of which are as 4:11. Find the larger angle.

Let the angle ABD be larger and its degree measure is equal to x degrees, then the angle CBD is smaller and its degree measure will be equal to (180 ° – x) degrees, since these two angles add up to the unfolded angle, that is, the angle, degree the measure of which is 180 °.

By the condition of the problem, the ratio of the degree measure of the larger to the degree measure of the smaller angle is (11/4).

Let’s compose and solve the equation:

x / (180 ° – x) = 11/4;

4 * x = 11 * (180 ° – x);

x = 132 °.

Answer: The degree measure of the larger angle is 132 °.