Question

What is mZJGK? I I к 870 2x–530 VI X+49º G X+13°

Answer 1

By definition, there are 360 degrees in a circle. Based on this and using the information given in the exercise, you can set up the following equation:

$m\angle JGK+m\angle JGI+m\angle IGH+m\angle HGK=360\degree$

You know that:

$\begin{gathered} m\angle JGK=x+49\degree \\ m\angle JGI=x+13\degree \\ m\angle IGH=2x-53\degree \\ m\angle HGK=87\degree \end{gathered}$

You need to substitute those expressions into the equation shown above:

$x+49\degree+x+13\degree+2x-53\degree+87\degree=360\degree$

Solve for "x":

$\begin{gathered} x+49\degree+x+13\degree+2x-53\degree+87\degree=360\degree \\ 4x+96\degree=360\degree \\ 4x=360\degree-96\degree \\ \\ x=\frac{264\degree}{4} \\ \\ x=66\degree \end{gathered}$

Now you can find the measure of the angle JGK as following:

$\begin{gathered} m\angle JGK=x+49\degree \\ m\angle JGK=66\degree+49\degree \\ m\angle JGK=115\degree \end{gathered}$

The answer is:

$m\angle JGK=115\degree$