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Tamar drew the figure below. She realized that she constructed complementary angles.

 
Which equation could be used to determine the value of x
​​​​​​​?
A.2x + 5x − 22 = 90

B.2x = 5x − 22

C.2x − 5x − 22 = 90

D.2x(5x − 22) = 90


The diagram shows two angles that are complementary, meaning their sum is 90 degrees. These angles are labeled as \( 2x \) and \( (5x - 22)^\circ \).

To find the value of \( x \), we know that complementary angles add up to 90 degrees. Therefore, we can set up the equation:

\[
2x + (5x - 22) = 90
\]

Simplifying this, we get:
\[
2x + 5x - 22 = 90
\]
\[
7x - 22 = 90
\]

Thus, the correct equation from the options is:

**A. \( 2x + 5x - 22 = 90 \)**

Would you like to see the detailed steps to solve for \( x \)?

Here are five related questions:
1. What is the value of \( x \) after solving the equation?
2. How do complementary angles relate to the sum of their measures?
3. What would the equation be if the angles were supplementary instead of complementary?
4. How can you check if two angles are complementary or supplementary using their measures?
5. If the angle \( GEF \) were given, how could you adjust the equation?

**Tip:** Complementary angles always sum to 90 degrees, while supplementary angles sum to 180 degrees.

Tamar drew the figure below. She realized that she constructed complementary angles. Which equation could be used to determine the value of x?

Learn how to solve for the variable x using complementary angles in geometry. This problem involves algebraic expressions and complementary angles theorem, suitable for students in Grades 7-9.

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