two angles, a and b are complementary if the sum of their measure is 90 degrees. If angle a is 21 degrees more than twice angle b find the measures of angles a and b. I would like to know how to set this equation up in order to find the answer.
The question defined what complementary angles are, but did not say that a and b are complementary.
The question has a solution if a and b are complementary, and will be assumed as follows.
if a and b are complementary, then
a+b=90
angle a is 21 degrees more than twice angle b means
a=21+2b
So with the two equations, you can solve for the two unknowns a and b.
To set up an equation to find the measures of angles a and b, we need to use the given information.
Let's start by representing the measure of angle b as "x". Now, according to the problem, angle a is 21 degrees more than twice angle b. So, we can represent angle a as "2x + 21".
Since the sum of angles a and b is 90 degrees (as they are complementary), we can write the equation as follows:
a + b = 90
Substituting the values we found for angles a and b:
(2x + 21) + x = 90
Simplifying the equation:
3x + 21 = 90
Now, to solve for x, we can isolate the variable by subtracting 21 from both sides:
3x = 90 - 21
3x = 69
Finally, we can solve for x by dividing both sides of the equation by 3:
x = 69 / 3
Calculating the result:
x = 23
So, angle b is 23 degrees.
To find angle a, we substitute this value back into the expression we found:
a = 2x + 21 = 2(23) + 21 = 46 + 21 = 67
Therefore, angle a is 67 degrees.
In conclusion, angle a measures 67 degrees and angle b measures 23 degrees.