The measure of one angle is 24 less than five times the measure of its supplement. Find each angle

Let's define the angles involved and set up the equation:

Let \( x \) represent the measure of one angle. Its supplement, by definition, would be \( 180^\circ - x \) since supplementary angles add up to \( 180^\circ \).

According to the problem, the measure of one angle is 24 less than five times the measure of its supplement. This can be written as the equation:

\[
x = 5(180^\circ - x) - 24
\]

Now, solve this equation step-by-step.

### Step 1: Distribute the 5
\[
x = 5 \times 180 - 5 \times x - 24
\]
\[
x = 900 - 5x - 24
\]

### Step 2: Simplify the right-hand side
\[
x = 876 - 5x
\]

### Step 3: Add \( 5x \) to both sides
\[
x + 5x = 876
\]
\[
6x = 876
\]

### Step 4: Divide both sides by 6
\[
x = \frac{876}{6}
\]
\[
x = 146
\]

So, one angle is \( 146^\circ \).

### Step 5: Find the supplement
\[
180^\circ - 146^\circ = 34^\circ
\]

Thus, the two angles are \( 146^\circ \) and \( 34^\circ \).

Would you like further details on the steps or clarifications?

Here are some related questions to consider:
1. What is the relationship between supplementary and complementary angles?
2. Can you solve for angles if given their complementary relationships instead?
3. How would you solve this problem if the angles were given in terms of degrees and radians?
4. What if the angles were not supplementary but formed a linear pair with a known ratio?
5. How does the solution change if one angle is more than five times its supplement?

**Tip:** Always check the conditions after solving an equation by plugging the solution back into the original expression to verify its correctness.

The measure of one angle is 24 less than five times the measure of its supplement. Find each angle.

Learn how to solve a problem involving two supplementary angles where one angle is 24 less than five times the other. This detailed step-by-step guide uses algebra to find the angle measures of 146° and 34°. Suitable for students in Grades 8-10.

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