SOLUTION: Can you explain to me what vertical, complementary, supplementary, alternate exterior and alternate interior angles?

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Question 767732: Can you explain to me what vertical, complementary, supplementary, alternate exterior and alternate interior angles?
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
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Vertical angles. Make an X shape on a piece of paper forming 4 angles. Pick one of the angles to start and number it 1, then number the rest in order around the X. The two odd numbered angles are vertical angles and the two even numbered angles are vertical angles. Vertical angles are ALWAYS equal to one another.

The sum of the measures of an angle and its complement is 90 degrees.

The sum of the measures of an angle and its supplement is 180 degrees.

Draw two parallel lines. The space between the two parallel lines is the "interior", the space that is not between the two parallel lines is the "exterior". Draw another line that intersects both of your parallel lines. We will call this line the "transversal" Where the transversal intersects the first of the two parallel lines, you have formed 4 angles. 2 of these angles are in the interior space, and the other 2 are in the exterior space. Same thing for the intersection of the transversal and the remaining parallel line. Angles that are on opposite sides of the transversal and associated with the other parallel line are "alteranate"

Pick one of the angles in the exterior area on one side of your diagram. Then go to the exterior area outside of the OTHER parallel line and on the OTHER side of the transversal. These two angles are "alternate exterior"

Similarly for "alternate interior". Pick an angle in the interior, go to the other side of the transversal on the interior of the other parallel line and you have chosen a pair of alternate interior angles.

John

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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Complementary angles:

Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees (right angle).
Supplementary angles:

Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees (straight line) .

Vertical angles:
Two pairs of angles are formed by two intersecting lines. Vertical angles are opposite angles in such an intersection. Vertical angles are equal to each other.
Alternate interior angles:
When a line intersects a pair of parallel lines alternate interior angles are formed. Alternate interior angles are equal to each other.
One way to find the alternate interior angles is to draw a zigzag line on the diagram. In the above diagrams, d and e are alternate interior angles. Similarly, c and f are also alternate interior angles.

Alternate Exterior Angles:
One way to remember alternate exterior angles is that they are the vertical angles of the alternate interior angles. Alternate exterior angles are equal to one another.





a and h are alternate exterior angles and they are equal to one another
b and g are alternate exterior angles and they are equal to one another
remaining angles are alternate interior angles