Question

problem 19: (first taught in lesson 15) 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 $x$ in the first - equation

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

Step3: Solve for $y$

Combine like terms: $5y=90^{\circ}$. Then $y=\frac{90^{\circ}}{5}=18^{\circ}$.

Step4: Solve for $x$

Since $x = 4y$, substitute $y = 18^{\circ}$ into it, we have $x = 4\times18^{\circ}=72^{\circ}$.

Answer:

$72^{\circ}$