Math Problem Statement

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

Solution

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 xx.

The larger angle is given by 5x+65x + 6.

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

Now, let's solve for xx.

x+5x+6=90x + 5x + 6 = 90 6x+6=906x + 6 = 90 6x=9066x = 90 - 6 6x=846x = 84 x=846=14x = \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!

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Math Problem Analysis

Mathematical Concepts

Complementary Angles
Linear Equations
Algebra

Formulas

Sum of complementary angles = 90°

Theorems

Complementary Angles Theorem

Suitable Grade Level

Grades 7-9