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The problem states that two angles are complementary, meaning the sum of their measures is 90°. It also says the larger angle is 6 more than five times the smaller angle.

Let the smaller angle be \( x \).

The larger angle is given by \( 5x + 6 \).

Since the two angles are complementary, their sum is 90°:
\[
x + (5x + 6) = 90
\]

Now, let's solve for \( x \).

\[
x + 5x + 6 = 90
\]
\[
6x + 6 = 90
\]
\[
6x = 90 - 6
\]
\[
6x = 84
\]
\[
x = \frac{84}{6} = 14
\]

So, the smaller angle is 14°.

Would you like more details or further explanation?

Here are 5 related questions to consider:
1. How would the equation change if the sum of the angles was 180° (supplementary)?
2. What would happen if the larger angle was described as 4 more than twice the smaller angle?
3. How would you solve the problem if you were given the difference between the angles instead of a sum?
4. Can complementary angles ever be equal? Why or why not?
5. What other geometric relationships involve angle pairs?

**Tip**: Always check your final answer by substituting the values back into the original equation to ensure accuracy!

Two angles are complementary. The larger angle is 6 more than five times the other. How large is the smaller angle?

Learn how to solve a problem involving complementary angles where the larger angle is 6 more than five times the smaller angle. This example covers key algebra concepts and suitable for Grades 7-9.

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