To convert the measure of an angle in degrees to an equivalent measure in radians, we multiply the measure in degrees by $\dfrac{\pi}{180}.$ This gives

\begin{align*} 40^\circ \cdot \left(\dfrac {\pi} {180^\circ} \right) &= \dfrac{40^\circ}{1} \cdot \left(\dfrac {\pi} {180^\circ} \right) \\[5pt] &= \dfrac{40^\circ}{180^\circ} \cdot \left(\dfrac {\pi} {1} \right) \\[5pt] &= \dfrac{40}{180} \cdot \left(\dfrac {\pi} {1} \right) \\[5pt] &= \dfrac{4}{18} \cdot \left(\dfrac {\pi} {1} \right) \\[5pt] &= \dfrac{2}{9} \cdot \left(\dfrac {\pi} {1} \right) \\[5pt] &= \dfrac {2\pi} {9} . \end{align*}

Therefore, $40^\circ$ is equivalent to $\dfrac {2\pi} {9}$ radians.

Notice that when we divide $40^\circ$ by $180^\circ,$ we can drop the degree $(\phantom{.}^\circ)$ symbol

To convert the measure of an angle in degrees to an equivalent measure in radians, we multiply the measure in degrees by $\dfrac{\pi}{180}.$ This gives

\begin{align*} 135^\circ \cdot \left(\dfrac {\pi} {180^\circ} \right) &= \dfrac{135^\circ}{1} \cdot \left(\dfrac {\pi} {180^\circ} \right) \\[5pt] &= \dfrac{135^\circ}{180^\circ} \cdot \left(\dfrac {\pi} {1} \right) \\[5pt] &= \dfrac{135}{180} \cdot \left(\dfrac {\pi} {1} \right) \\[5pt] &= \dfrac{3}{4} \cdot \left(\dfrac {\pi} {1} \right) \\[5pt] &= \dfrac {3\pi} {4} . \end{align*}

Therefore, $135^\circ$ is equivalent to $\bbox[4pt,border: 1px solid lightgray]{\dfrac {3\pi} {4}}$ radians.

Notice that when we divide $135^\circ$ by $180^\circ,$ we can drop the degree $(\phantom{.}^\circ)$ symbol.

A full rotation equals $360^\circ$, which is equivalent to $2\pi$ radians.

Therefore, one-half of a full rotation will be $\dfrac{360^\circ}{2} = 180^\circ.$

Converting this to radians, we get

\begin{align*} \dfrac{\pi}{180^\circ} \cdot 180^\circ &=\dfrac{\pi}{180^\circ} \cdot \dfrac{180^\circ}{1}\\[5pt] &=\dfrac{\pi}{1} \cdot \dfrac{180^\circ}{180^\circ}\\[5pt] &=\dfrac{\pi}{1} \cdot \dfrac{1}{1}\\[5pt] &=\pi. \end{align*}

To convert the measure of an angle in radians to an equivalent measure in degrees, we multiply the measure in radians by $\dfrac{180^\circ}{\pi}.$ This gives

\begin{align*} \require{cancel} \left(\dfrac{\pi}{8}\right) \cdot \left(\dfrac {180^\circ} {\pi}\right) &= \dfrac {180^\circ\cdot\pi} {8\cdot\pi} \\[5pt] &= \dfrac {180^\circ\pi} {8\pi} \\[5pt] &= \dfrac {180^\circ\cancel{\pi}} {8\cancel{\pi}} \\[5pt] &= \dfrac {180^\circ} {8} \\[5pt] &= 22.5^\circ. \end{align*}

Therefore, $\dfrac{\pi}{8}$ is equivalent to $22.5^\circ.$

To convert the measure of an angle in radians to an equivalent measure in degrees, we multiply the measure in radians by $\dfrac{180^\circ}{\pi}.$ This gives

\begin{align*} \require{cancel} \left({2\pi}\right) \cdot \left(\dfrac {180^\circ} {\pi}\right) &= \dfrac {2\cdot180^\circ\cdot\pi} {\pi} \\[5pt] &= \dfrac {360^\circ\pi} {\pi} \\[5pt] &= \dfrac {360^\circ\cancel{\pi}} {\cancel{\pi}} \\[5pt] &= {360^\circ}. \end{align*}

Therefore, ${2 \pi}$ is equivalent to $360^\circ.$

To convert the measure of an angle in radians to an equivalent measure in degrees, we multiply the measure in radians by $\dfrac{180^\circ}{\pi}.$ This gives \[ 0.957 \cdot \dfrac{180^\circ}{\pi} \approx 54.83^\circ, \] rounded to $2$ decimal places. Therefore, $0.957$ radians is equal to $55^\circ$ to the nearest degree.

To convert the measure of an angle in radians to an equivalent measure in degrees, we multiply the measure in radians by $\dfrac{180^\circ}{\pi}.$ This gives

$$ \dfrac{6\pi}{13} \cdot \dfrac{180^\circ}{\pi} \approx 83.077^\circ, $$ rounded to $3$ decimal places.

Therefore, $\dfrac{6\pi}{13}$ radians is equal to $\bbox[4pt,border: 1px solid lightgray]{ 83^\circ}$ to the nearest degree.

To convert the measure of an angle in degrees to an equivalent measure in radians, we multiply the measure in degrees by $\dfrac{\pi}{180^\circ}.$ This gives \[ 99^\circ \cdot \dfrac{\pi}{180^\circ} \approx 1.728, \] rounded to $3$ decimal places.

Hence, the angle $99^\circ$ is equal to $\bbox[4pt,border: 1px solid lightgray]{ 1.7}$ radians rounded to one decimal place.

To convert the measure of an angle in degrees to an equivalent measure in radians, we multiply the measure in degrees by $\dfrac{\pi}{180^\circ}.$ This gives \[ 48.6^\circ \cdot \dfrac{\pi}{180^\circ} \approx 0.848, \] rounded to $3$ decimal places.

Hence, the angle $48.6^\circ$ is equal to $0.8$ radians rounded to one decimal place.