Question

Angles BCD and DCE are complementary ( add up to 90 degrees ). If < BCD = 63 and < DCE = 4.5x, what is the value of x? Set up an equation and solve A: x= 14 B: x= 27 C: x= 90;D: x= 6

Answer 1

We know that angles BCD and DCE are complementary, meaning their measures add up to 90 degrees. We can set up the equation based on the information given:

\[
\text{Angle BCD} + \text{Angle DCE} = 90
\]

Given that:

\[
\text{Angle BCD} = 63 \text{ degrees}
\]
\[
\text{Angle DCE} = 4.5x
\]

Substituting these values into the equation, we get:

\[
63 + 4.5x = 90
\]

Now, we will solve for \(x\):

1. Subtract 63 from both sides:

\[
4.5x = 90 - 63
\]
\[
4.5x = 27
\]

2. Now, divide both sides by 4.5:

\[
x = \frac{27}{4.5}
\]
\[
x = 6
\]

Thus, the value of \(x\) is \(6\).

The correct answer is **D: x = 6**.