Question

The figure is not drawn to scale. Find the Value of

Answer 1

We know that the ratio of angles f and g is 2:1, this means that:

$f=2g$

Now that we know that we notice that all the angles have to add to 360°, then we have the equation:

$\begin{gathered} f+106+g+56=360 \\ f+g+162=360 \\ f+g=198 \end{gathered}$

Plugging the equation relating f anf g we have that:

$\begin{gathered} 2g+g=198 \\ 3g=198 \\ g=\frac{198}{3} \\ g=66 \end{gathered}$

Now that we know the value of g we plug it on the first equation, then:

$\begin{gathered} f=2(66) \\ f=132 \end{gathered}$

Therefore:

$m\angle f=132$