The m angle A is 30 more than twice angle B. If angle A and angle B form a linear pair, find the measure of both angles.
Angle A is 30 more than twice angle B can be written as
A = 2B + 30
Because we know that angle A and angle B form a linear pair, we know that
A + B = 180
Plug the first equation into the second equation and solve for A. Once you solve for A, plug the know A value into into second equation and solve for B.
To solve this problem, let's first define the variables:
Let angle A be denoted as 'x'
Let angle B be denoted as 'y'
According to the information given, we know that angle A is 30 more than twice angle B. Therefore, we can write the equation as:
x = 2y + 30
We also know that angle A and angle B form a linear pair, which means they are adjacent angles that add up to 180 degrees. So, we can write another equation as:
x + y = 180
Now, we can solve this system of equations to find the values of x and y.
Substitute the value of x from the first equation into the second equation:
(2y + 30) + y = 180
3y + 30 = 180
Next, isolate the variable:
3y = 180 - 30
3y = 150
Now, divide both sides of the equation by 3 to solve for y:
y = 150 / 3
y = 50
Substitute this value of y back into the first equation to find x:
x = 2y + 30
x = 2(50) + 30
x = 130
Therefore, angle A (x) measures 130 degrees and angle B (y) measures 50 degrees.