Beam BD divides the unfolded angle ABC into two angles ABC and DBC. Find the degree measure

Beam BD divides the unfolded angle ABC into two angles ABC and DBC. Find the degree measure of these angles if the angle ABD is 1.5 times the angle DBC

It is known from the condition that the beam BD divides the unfolded angle ABC into two angles, DBC and ABD. ABD is 1.5 times the DBC angle.

Let x be the degree measure of the DBC angle.
Let 1.5x be the degree measure of the angle ABD.
the unfolded angle is always 180 degrees.

Let’s compose and solve the equation.

1.5x + x = 180;
2.5x = 180;
x = 72 (degrees) is the degree measure of the DBC angle.

Now we can calculate the degree measure of the angle ABD.

72 * 1.5 = 108 (degrees) – the degree measure of the ABD angle.

Answer: The degree measure of the ABD angle is 108 degrees, the degree measure of the DBC angle is 72 degrees.