Two angles are complementary. The larger angle measures 6 more than three times the smaller angle. Write an equation that can be used to find out the measures of both angles then simplify
4x+6=90
4x=84
x=21
The smaller angle is 21 degrees
The larger angle is 69 degrees
To solve this problem, we need to set up an equation based on the given information.
Let's assume that the smaller angle measures x degrees. Then, the larger angle can be expressed as 3x + 6, as it is 6 more than three times the smaller angle.
Since the two angles are complementary, their sum is equal to 90 degrees.
Therefore, we can write the equation as:
x + (3x + 6) = 90
Now, let's simplify the equation and solve for x:
Combining like terms:
4x + 6 = 90
Subtracting 6 from both sides:
4x = 84
Dividing both sides by 4:
x = 21
So, the smaller angle measures 21 degrees.
To find the larger angle, we substitute x back into the expression 3x + 6:
3(21) + 6 = 63 + 6 = 69
Therefore, the larger angle measures 69 degrees.
In summary, the smaller angle measures 21 degrees, and the larger angle measures 69 degrees.
x + 3x + 6 = 90
Solve for x to find the smaller angle.