Write an equation that can be used to solve the problem. Find the solution to the problem. Angles A and B are complementary angles. Determine the measures of angles A and B if angle A is 29 times the size of angle B. What is the measure of angle​ A? 

To solve this problem, we can set up an equation based on the fact that angles A and B are complementary, meaning their measures add up to \(90^\circ\).

Let:
- \(B = x\), which represents the measure of angle B.
- \(A = 29x\), since angle A is 29 times the size of angle B.

Since angles A and B are complementary, their measures add up to \(90^\circ\). This gives the equation:

\[
A + B = 90^\circ
\]

Substituting \(A = 29x\) and \(B = x\) into the equation:

\[
29x + x = 90
\]

Simplify:

\[
30x = 90
\]

Solve for \(x\):

\[
x = \frac{90}{30} = 3
\]

Now that we know \(x = 3\), we can find the measures of angles A and B:

- \(B = x = 3^\circ\)
- \(A = 29x = 29 \times 3 = 87^\circ\)

Thus, the measure of angle A is \(87^\circ\) and the measure of angle B is \(3^\circ\).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the sum of two complementary angles?
2. If angle A was 5 times the size of angle B, how would the equation change?
3. How would you solve for two supplementary angles with a similar condition?
4. Can two complementary angles be equal in measure? If so, what are their values?
5. What happens if angles A and B were in degrees and radians?

**Tip**: Always check your equation setup with the conditions provided to ensure accuracy.

Write an equation that can be used to solve the problem. Find the solution to the problem. Angles A and B are complementary angles. Determine the measures of angles A and B if angle A is 29 times the size of angle B. What is the measure of angle​ A?

Learn how to solve the complementary angles problem where angle A is 29 times the size of angle B. This step-by-step guide covers the algebraic equation setup and solution, perfect for students in Grades 6-8. Understand how to apply the Complementary Angles Theorem and solve for angle A.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation