## Related questions with answers

Suppose angles A and B are a linear pair. Given the relationships below, find the measure of angles A and B. Round your answers to the nearest tenth of a degree. $m \angle A=3 x+7^{\circ} ; m \angle B=5 x+20^{\circ}$

Solution

VerifiedA linear pair consists of adjacent angles that form a straight angle so they are supplementary. Hence, we can write:

$m\angle A+m\angle B=180\text{\textdegree}$

$(3x+7\text{\textdegree})+ (5x+20\text{\textdegree})=180\text{\textdegree}$

$8x+27\text{\textdegree}=180\text{\textdegree}$

$8x =153\text{\textdegree}$

$x =\dfrac{153\text{\textdegree}}{8}$

$x =19.125\text{\textdegree}$

So, the measures of the angles are:

$\begin{align*} m\angle A&=3(19.125\text{\textdegree})+7\text{\textdegree} \approx \color{#c34632}64.4\text{\textdegree}\\ m\angle B&=5(19.125\text{\textdegree})+20\text{\textdegree} \approx \color{#c34632}115.6\text{\textdegree} \end{align*}$

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