"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 "<u>bisects</u>" 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 '<u>bisect</u>or'. 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° .
