Two angles are adjacent and form an angle of 150degree. The larger angle is 30 degree more than twice the smaller angle.find the angles

x + 2x+30 = 150

Please give full explaination

To solve this problem, let's denote the smaller angle as "x" degrees.

According to the problem, the larger angle is 30 degrees more than twice the smaller angle. So, we can express the larger angle as 2x + 30 degrees.

Now, we know that the sum of adjacent angles is 150 degrees. Therefore, we can set up the equation:

x + (2x + 30) = 150

Simplifying the equation, we combine like terms:

3x + 30 = 150

Next, we isolate the variable by subtracting 30 from both sides of the equation:

3x = 150 - 30

Simplifying further:

3x = 120

To solve for x, we divide both sides of the equation by 3:

x = 120 / 3

x = 40

So, the smaller angle is 40 degrees.

To find the larger angle, substitute the value of x (smaller angle) into the expression for the larger angle:

2x + 30 = 2(40) + 30 = 80 + 30 = 110

Therefore, the larger angle is 110 degrees.

In summary, the smaller angle is 40 degrees, and the larger angle is 110 degrees.