Special Angle Pairs

Vertical Angles

When 2 lines intersect, they form 4 angles:

verticalAnim.GIF

Vertical angles are angles that are opposite each other:

vertical2Anim.GIF

Consecutive pairs of angles form a line, so they add to 180o. They are called a linear pair. If one angle measures 30o, then its adjacent angles measure 180o − 30o = 150o, so they are equal. Likewise if an angle measures 150o, then its adjacent angles measure 30o, so they are equal. In other words, we have gone in a circle, and vertical angles will always be equal.

vertical3Anim.GIF

 

Complementary and Supplementary Angles

Two angles are complementary if their measures add to 90o. Each is said to be the complement of the other.

Two angles are supplementary if their measures add to 180o. Each is said to be the supplement of the other. When two angles form a linear pair, then they are supplementary. But "supplementary" doesn't refer to just linear pairs. Any two angles whose measures add to 180o are supplementary.

 

Problem 1

Problem1Q.gif

Solution

Problem1A.gif

 

Problem 2

Problem2Q.gif

Solution

Problem2A.gif

 

Problem 3

Problem3Q.gif

Solution

Problem3A.gif

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