Question

Challenge: Draw the diagram. Then solve the problem.G lies on the interior of

Answer 1

It is given that G lies in the interior of angle OMS.

$\angle OMG=(4x+1)^{\circ},\angle GMS=(2x-2)^{\circ},\angle OMS=125^{\circ}$

The diagram with the information is shown below:

From the figure it can be seen that the angle OMS is the sum of OMG and GMS so it follows:

$\begin{gathered} \angle OMS=\angle OMG+\angle GMS \\ 125=4x+1+2x-2 \\ 125=6x-1 \\ 6x=126 \\ x=\frac{126}{6} \\ x=21 \end{gathered}$

So the value of angle OMG is given by:

$\angle OMG=4x+1=4\times21+1=85^{\circ}$

Hence angle OMG is 85 degrees.