Straight angles Are extremely important in geometry. When two lines intersect , they form multiple angles. In the diagram below,

When two straight lines cross, the vertically opposite angles created are equal, and the remaining two angles match each other as well. Suppose one known angle is x; then the two adjacent angles can be calculated by subtracting twice x from 360 degrees and dividing the remainder by 2.

Thus, the table fills out as follows:

Row 1:

Given angle <GEF = 120°

Angle <FEM is adjacent to <GEF, so


Angle <MEH is vertically opposite to <GEF, making it equal to 120°

Angle <HEG is vertically opposite <FEM, so it equals 60°.


Row 2:

Given angle <MEH = 150°

Since <MEH is vertically opposite to <GEF, <GEF = 150°

Angle <FEM is adjacent to <GEF, thus


Angle <HEG is vertically opposite to <FEM, so <HEG = 30°.


Row 3:

Given angle <FEM = 25°

Angle <FEM is adjacent to <GEF, thus


Angle <MEH is vertically opposite to <GEF, equal to 155°

Angle <HEG is vertically opposite <FEM, so it equals 25°.


Row 4:

Given angle <HEG = 45°

Angle <HEG is adjacent to <GEF, so


Angle <FEM is vertically opposite to <HEG and thus equals 45°

Angle <MEH is vertically opposite to <GEF, hence <MEH = 135°.