The measure of an angle is nine times the measure of its complement. Find the measure of each angle.

The smaller angle measures 
 º .

The larger angle measures 


Let the measure of the smaller angle be \( x \).

Since the angle is complementary, its complement is \( 90^\circ - x \).

According to the problem, the measure of the larger angle is nine times the measure of the smaller angle, so:

\[
90^\circ - x = 9x
\]

Now, solve for \( x \):

\[
90^\circ = 10x
\]
\[
x = \frac{90^\circ}{10} = 9^\circ
\]

Thus, the smaller angle measures \( 9^\circ \).

To find the larger angle, substitute \( x = 9^\circ \) into \( 90^\circ - x \):

\[
90^\circ - 9^\circ = 81^\circ
\]

So, the larger angle measures \( 81^\circ \).

### Final Answer:
- The smaller angle measures \( 9^\circ \).
- The larger angle measures \( 81^\circ \).

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the sum of two complementary angles?
2. How do you define complementary and supplementary angles?
3. Can an obtuse angle ever be part of a complementary pair?
4. What are complementary angles used for in geometry problems?
5. How would the problem change if the larger angle was eight times the smaller angle?

**Tip:** In complementary angle problems, always remember that their sum is exactly \( 90^\circ \).

The measure of an angle is nine times the measure of its complement. Find the measure of each angle.

Discover how to solve a problem where the measure of one angle is nine times the measure of its complement. Learn how to use basic algebraic techniques to find that the smaller angle measures 9° and the larger angle measures 81°. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation