Question

in her math notebook, amanda divided an angle into 2 same - sized angles. each new angle measured 55°. let m represent the measure of the original angle. which equation models the problem? \\(2m = 55\\) \\(\frac{m}{2}=55\\) solve this equation to find the measure of the original angle.

Explanation:

Step1: Identify the correct equation

The original angle \( m \) is divided into 2 same - sized angles. So each angle is \( \frac{m}{2} \), and we know each new angle measures \( 55^\circ \). So the equation that models the problem is \( \frac{m}{2}=55 \).

Step2: Solve the equation for \( m \)

To solve \( \frac{m}{2}=55 \), we multiply both sides of the equation by 2.
\[

$$\begin{align*} \frac{m}{2}\times2&=55\times2\\ m& = 110 \end{align*}$$

\]

Answer:

The equation that models the problem is \( \frac{m}{2}=55 \), and the measure of the original angle \( m \) is \( 110^\circ \).