Question

the measure of an angle is thirty - five times the measure of its supplementary angle. what is the measure of each angle? ° and °

Explanation:

Step1: Define the angles

Let the measure of the angle be $x$ and its supplementary angle be $y$. We know that $x + y=180^{\circ}$ (by the definition of supplementary angles), and $x = 35y$.

Step2: Substitute $x$ in the first - equation

Substitute $x = 35y$ into $x + y=180^{\circ}$, we get $35y+y = 180^{\circ}$.
Combining like - terms, $36y=180^{\circ}$.

Step3: Solve for $y$

Divide both sides of the equation $36y = 180^{\circ}$ by 36: $y=\frac{180^{\circ}}{36}=5^{\circ}$.

Step4: Solve for $x$

Since $x = 35y$, substitute $y = 5^{\circ}$ into this equation, then $x=35\times5^{\circ}=175^{\circ}$.

Answer:

$175$ and $5$