Complementary Angles Worksheet - Solve for angle x in right angles.

Let's solve each problem on the Complementary Angles worksheet.

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🔹 What are Complementary Angles?

Two angles are complementary if their measures add up to 90 degrees.
So, if one angle is given, you can find the other by subtracting from 90:

> $ x = 90^\circ - \text{given angle} $

Each diagram shows a right angle (90°) split into two angles: one labeled and the other as $ x $. We need to find $ x $ in each case.

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✔ Let's solve each one:

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1.
Given: One angle is $ 30^\circ $
$ x = 90 - 30 = 60^\circ $
✔ Already solved: $ \boxed{60} $

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2.
Given: One angle is $ 25^\circ $
$ x = 90 - 25 = 65^\circ $
✔ $ \boxed{65} $

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3.
Given: One angle is $ 55^\circ $
$ x = 90 - 55 = 35^\circ $
✔ $ \boxed{35} $

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4.
Given: One angle is $ 15^\circ $
$ x = 90 - 15 = 75^\circ $
✔ $ \boxed{75} $

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5.
Given: One angle is $ 50^\circ $
$ x = 90 - 50 = 40^\circ $
✔ $ \boxed{40} $

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6.
Given: One angle is $ 63^\circ $
$ x = 90 - 63 = 27^\circ $
✔ $ \boxed{27} $

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7.
Given: One angle is $ 62^\circ $
$ x = 90 - 62 = 28^\circ $
✔ $ \boxed{28} $

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8.
Given: One angle is $ 45^\circ $
$ x = 90 - 45 = 45^\circ $
✔ $ \boxed{45} $

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9.
Given: One angle is $ 80^\circ $
$ x = 90 - 80 = 10^\circ $
✔ $ \boxed{10} $

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✔ Final Answers:

1. $ x = 60 $
2. $ x = 65 $
3. $ x = 35 $
4. $ x = 75 $
5. $ x = 40 $
6. $ x = 27 $
7. $ x = 28 $
8. $ x = 45 $
9. $ x = 10 $

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📝 Explanation Summary:

All these problems involve complementary angles, meaning the two angles together form a right angle (90°). So, to find the missing angle $ x $, we use:

$$
x = 90^\circ - \text{(known angle)}
$$

This is a fundamental concept in geometry and helps in understanding angle relationships in triangles, rectangles, and more.

Let me know if you'd like this turned into a printable answer key!