Two angles are complementary. The measure of the larger angle is 14° less than 3 times the measure of the smaller angle.

The measure of the smaller angle is _________
 degrees and the measure of the larger angle is ______
 degrees.

Let the measure of the smaller angle be \( x \) degrees. Since the two angles are complementary, their sum is 90°. According to the problem, the larger angle is 14° less than 3 times the smaller angle, so the larger angle can be represented as \( 3x - 14 \) degrees.

We can set up the following equation for the sum of the angles:

\[
x + (3x - 14) = 90
\]

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

\[
x + 3x - 14 = 90
\]
\[
4x - 14 = 90
\]
\[
4x = 104
\]
\[
x = 26
\]

So, the smaller angle is 26°.

To find the larger angle, substitute \( x = 26 \) into \( 3x - 14 \):

\[
3(26) - 14 = 78 - 14 = 64
\]

Thus, the smaller angle is 26° and the larger angle is 64°.

Would you like more details on how this was solved?

Here are 5 related questions to expand your understanding:
1. What is the definition of complementary angles?
2. How would you solve for two angles if they were supplementary instead?
3. Can you express the relationship between complementary angles algebraically in another way?
4. What happens if the larger angle was 14° more than 3 times the smaller angle?
5. How can you verify your solution in angle problems?

**Tip:** Always double-check your final result by verifying that the angles satisfy the original condition.

Two angles are complementary. The measure of the larger angle is 14° less than 3 times the measure of the smaller angle. The measure of the smaller angle is _________ degrees and the measure of the larger angle is ______ degrees.

Learn how to solve a complementary angles problem where the larger angle is 14° less than 3 times the smaller angle. Detailed step-by-step solution using algebraic equations. Suitable for students in Grades 6-8.

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