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.