Question

Find the measurements of angle BEC using the figure below . Remember that two angles on a straight line should equal 180

Answer 1

$m\angle BEC=70^{\circ^{}^{}}$

1) As we can see there is a linear pair with the angles ∠BEC and ∠CEF these angles are supplementary. So we can write out the following equation:

$\begin{gathered} 3x-5+4x+10=180 \\ 7x+5=180 \\ 7x=180-5 \\ 7x=175 \\ \frac{7x}{7}=\frac{175}{7} \\ x=25 \end{gathered}$

2) So now that we know the quantity of x. Let's plug x=25 into the angle ∠BEC formula:

$m\angle BEC=3(25)-5=70$