Adjacent, Vertical, Supplementary, and Complementary Angles

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Presentation transcript:

Adjacent, Vertical, Supplementary, and Complementary Angles

Adjacent angles: Two angles are adjacent if they share a common vertex and side but have no common interior points. 15º 45º

Examples of adjacent angles. 35º 45º 80º 55º 130º 50º 85º 20º

These angles are NOT adjacent. 35º 100º 50º 35º 55º 45º

When 2 lines intersect, they make vertical angles. 75º 105º 105º 75º

Vertical angles are opposite to one another. 45º 75º 135º 135º 105º 105º 45º 75º

Vertical angles are congruent (equal). Two angles are vertical angles if their sides form two pairs of opposite rays. The sum of the measures of angles that form a linear pair is 180°. 150º 30º 150º 30º

Supplementary angles : Two angles are Supplementary angles if the sum of their measures is 90°. Each angle is the Supplement of the other. Supplementary angles can be adjacent or nonadjacent. 40º 120º 60º 140º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

Complementary angles : Two angles are Complementary angles if the sum of their measures is 90°. Each angle is the complement of the other. Complementary angles can be adjacent or nonadjacent. 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Angles but not Adjacent

Practice Time!

Directions: Identify each pair of angles as vertical, supplementary, complementary, or none of the above.

120º 60º

120º + 60º = 180º Supplementary Angles

60º 30º

30º + 60º = 90º Complementary Angles

75º 75º

Vertical Angles

60º 40º

THINK AGAIN! None of the above

60º 60º

Vertical Angles

135º 45º

Sure Check Again! 135º + 45º = 180º Supplementary Angles

25º 65º

Sure Check Again! 25º + 65º = 90º Complementary Angles

90º 40º 50º

Complementary Angles Sure Check Again! 50º + 90º + 40º = 180º Is it a pair? Oops! NO None of the above

Directions: Determine the missing angle.

?º 45º

Working: Supplementary Angles 180º - 45º = 135º

?º 65º

Working: Complementary Angles 90º - 65º = 25º

?º 35º

Working: Vertical Angles so 35º

?º 50º

Working: Supplementary Angles 130º + 50º = 180º 130º 50º

?º 140º

Working: Vertical Angles so 140º

?º 40º

Working: Complementary Angles 90º - 40º = 50º