Question

Suppose you know that ∠S and ∠Y are complementary, and that m∠S = 4(m∠Y) − 135°. Find m∠Y.

The value of m∠Y is

Answer 1

The value of m∠Y is 45°, determined by using the relationship that angles S and Y are complementary and by setting up and solving the equation 4(m∠Y) - 135° + m∠Y = 90°.

Step-by-step explanation:

To find the value of m∠Y, we can use the given information that ∠S and ∠Y are complementary, and that m∠S = 4(m∠Y) - 135°.

Since ∠S and ∠Y are complementary, their sum is 90°.

So we can set up the equation m∠Y + 4(m∠Y) - 135° = 90° and solve for m∠Y.

Combining like terms, we get 5(m∠Y) = 225°.

Dividing both sides by 5, we find that m∠Y = 45°.