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.