Question

Find the value of x. 128 degrees 138 degrees 540 degrees 64 degrees

Answer 1

We have the following:

We know that in the corners there is an exterior angle and an interior angle, in both cases, the sum of both angles is equal to 180 °

Therefore, we can calculate all the internal angles like this

$\begin{gathered} 80+y=180\Rightarrow y=180-80=100 \\ 42+z=180\Rightarrow z=180-42=138 \end{gathered}$

We know that the sum of the angles of a pentagon is the following

(5 - 2) · 180 ° = 540º

We know that the sum of the angles of a pentagon is the following (5 - 2) · 180 ° = 540º.

$540=100+110+x+138+2x$

now, resolving for x:

$\begin{gathered} x+2x=540-100-110-138 \\ 3x=192 \\ x=\frac{192}{3} \\ x=64 \end{gathered}$

So the value of x is 64 degrees