Set up a system to solve. Two angles are complementary. Four times one angle is equal to the other angle plus 10. Find the two angles.
The answer is x=20 and y=70 but I don't know how they got the answer..
as with the supplementary angles problem,
4x = (90-x)+10
To solve this system of equations, let's assign variables to the unknown angles. Suppose one angle is A and the other is B.
Given:
1) Two angles are complementary, which means their sum is 90 degrees: A + B = 90
2) Four times one angle is equal to the other angle plus 10: 4A = B + 10
To find the values of A and B, we can use substitution or elimination method. Let's use substitution:
From equation 2, we can isolate B by subtracting 10 from both sides: B = 4A - 10
Now, substitute the value of B in equation 1:
A + (4A - 10) = 90
Combine like terms:
5A - 10 = 90
Add 10 to both sides:
5A = 100
Divide both sides by 5:
A = 20
Now, substitute the value of A into equation 2 to find B:
B = 4(20) - 10
B = 80 - 10
B = 70
Hence, the two angles are A = 20 degrees and B = 70 degrees.