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Problem 24

# The measure of the complement of a given angle is four times the measure of the angle. Find the measure of the given angle.

Expert verified
The measure of the given angle is 18 degrees.
See the step by step solution

## Step 1: Knowing what Complementary Angles Are

Firstly, it's important to know that in a pair of complementary angles, one angle is the complement of the other, which simply means that the two angles add up to 90 degrees.

## Step 2: Setting Up the Equation

According to the given exercise, we know that the complement of the angle is four times the measure of the angle itself. If we call the measure of the angle $$x$$, then the complement is $$4x$$. From what we know about complementary angles, we have: $$x + 4x = 90$$

## Step 3: Simplifying the Equation

Now, let's simplify this equation. Combining like terms, we get: $$5x = 90$$

## Step 4: Solving the Equation

To get $$x$$ by itself, we need to divide both sides of the equation by 5: $$x = \frac{90}{5}$$

## Step 5: Calculating the Angle Measure

Doing the division, we find: $$x = 18$$ So, the measure of the given angle is 18 degrees. It's always a good idea to double-check your work, so you can do so by substititing $$x = 18$$ back into the original equation and confirming that it yields a true statement.

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