Find m∠EGF. please help!

We're provided - ∠AGB = 30° , ∠ DGC = 50° and ∠ EGF = 2x. We're asked to find out m ∠ EGF.Note that ∠ AGB , ∠ BGC and ∠ DGC form a straight line which means that their sum is equal to 180°.When two lines intersect , the angles formed opposite to each other are called verticall opposite angles. Vertically opposite angle are always equal to each other.

Re-read the second point which I have mentioned above. Now , Set up an equation and solve for ∠ BGC .

[ Sum of angle in a straight line ]

Hence , m ∠ BGC = 100°. Now , Re-read the third point which I have mentioned above and set up an equation and solve for x.

[ being vertically opposite angles ]

The value of x is 50°. Now :

Hence , Our final answer is 100° . And we're done!

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁