Question

Find the value of x.
1. 21°, 2. x and 3. 55°
x = [?]°

Answer 1

To find the value of \( x \) in the sequence \( 21^\circ, x, 55^\circ \), we can assume that these angles are part of an arithmetic sequence. In an arithmetic sequence, the difference between consecutive terms is constant.

Let the common difference be \( d \). We can express the relationships as follows:

1. \( x - 21 = d \)
2. \( 55 - x = d \)

Since both equations are equal to \( d \), we can set them equal to each other:

\[
x - 21 = 55 - x
\]

Now, solve for \( x \):

1. Add \( x \) to both sides:

\[
x + x - 21 = 55
\]

2. Combine the \( x \) terms:

\[
2x - 21 = 55
\]

3. Add 21 to both sides:

\[
2x = 55 + 21
\]
\[
2x = 76
\]

4. Divide by 2:

\[
x = \frac{76}{2}
\]
\[
x = 38
\]

Thus, the value of \( x \) is \( 38^\circ \).