Question

I have no idea how to do these geometry problems! if someone could explain to me how to do them that'd be awesome!

Answer 1

"BISECT" an angle means split it into two equal angles.

In this diagram, you can see the long line  GH,  and they're telling us that  GH  "bisects" the big angle.  That means that the angles on both sides of line GH are equal ... their measures are the same number of degrees.  

Now, in the diagram, those angles on each side of  GH  are labeled.  On one side, the angle is labeled  3x-3  and on the other side the angle is labeled  4x-14 .  We don't know the measure of these angles because we don't know what ' x ' is.  BUT ... we know that the two angles are EQUAL, because GH is a 'bisector'.  Maybe we can use this clue to find ' x '.

We know their measures are equal, so we can write ...

3x - 3  =  4x - 14

Subtract  3x  from each side:  -3  =  x - 14

Add  14  to each side:    11  =  x

Look at that !  Is that cool or what ! ?  ' x ' is 11 .

So the angle above GH is  3x-3 . . . that's 30°

and the angle below GH is  4x-14 . . . that's also 30° .

Yay !  They really ARE equal.

Now let's look back at the question:

a).  'x' is 11° .  Angle FGH is the angle above GH, that's 30° .

b).  Angle HGI is the angle below GH, that's also 30° .

c).  Angle FGI is the whole big angle.  That's 30° + 30° = 60° .