Question

problem 19: an angle has four times the measure of its complement. what is the measure of the angle? after you enter your answer press go.

Explanation:

Step1: Define variables

Let the angle be $x$ and its complement be $y$. We know that $x + y=90^{\circ}$ (by the definition of complementary - angles), and $x = 4y$.

Step2: Substitute

Substitute $x = 4y$ into $x + y=90^{\circ}$. We get $4y+y=90^{\circ}$.

Step3: Combine like - terms

Combining like - terms in $4y + y=90^{\circ}$, we have $5y=90^{\circ}$.

Step4: Solve for $y$

Dividing both sides of $5y=90^{\circ}$ by 5, we get $y=\frac{90^{\circ}}{5}=18^{\circ}$.

Step5: Solve for $x$

Since $x = 4y$, substituting $y = 18^{\circ}$ into this equation, we get $x=4\times18^{\circ}=72^{\circ}$.

Answer:

$72^{\circ}$