Question

the measure of an angle is fourteen times the measure of its complementary angle. what is the measure of each angle? ° and °

Explanation:

Step1: Define the angles

Let the measure of the angle be $x$ and its complementary angle be $y$. We know that $x + y=90^{\circ}$ (by the definition of complementary angles), and $x = 14y$.

Step2: Substitute $x$ in the first - equation

Substitute $x = 14y$ into $x + y=90^{\circ}$, we get $14y+y=90^{\circ}$.

Step3: Combine like - terms

$15y = 90^{\circ}$.

Step4: Solve for $y$

$y=\frac{90^{\circ}}{15}=6^{\circ}$.

Step5: Solve for $x$

Since $x = 14y$, then $x=14\times6^{\circ}=84^{\circ}$.

Answer:

$84$ and $6$