Two complementary angles are drawn such that one angle is 10 degree more than seven times the other angle. find the measure of each angle
AAAaannndd the bot gets it wrong yet again!
complementary angles sum to 90.
This is just insane.
To find the measure of each angle, let's assign variables to represent the angles.
Let:
- x be the measure (in degrees) of the first angle
- y be the measure (in degrees) of the second angle
According to the given information, one angle is 10 degrees more than seven times the other angle. This can be written as an equation:
x = 7y + 10 (Equation 1)
Additionally, since the two angles are complementary, their sum is 90 degrees:
x + y = 90 (Equation 2)
We can now solve this system of equations to determine the values of x and y.
Substituting the value of x from Equation 1 into Equation 2, we have:
7y + 10 + y = 90
Combining like terms:
8y + 10 = 90
Now, subtracting 10 from both sides:
8y = 80
Dividing both sides by 8:
y = 10
Substituting this value back into Equation 1 to find x:
x = 7(10) + 10
x = 70 + 10
x = 80
Therefore, the measure of the first angle is 80 degrees, and the measure of the second angle is 10 degrees.
Let x be the measure of the smaller angle.
Then the measure of the larger angle is (7x + 10).
Therefore, x + (7x + 10) = 180
8x + 10 = 180
8x = 170
x = 21.25
The measure of the smaller angle is 21.25 degrees and the measure of the larger angle is (7x + 10) = 148.25 degrees.