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Complementary and Supplementary Angles
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These two angles are complementary.
Complementary Angles Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. Example: These two angles are complementary.
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These two angles can be "pasted" together to form a right angle!
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These two angles are supplementary.
Supplementary Angles Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees. Example: These two angles are supplementary.
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These two angles can be "pasted" together to form a straight line!
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Complementary and Supplementary
Find the missing angle. 1. Two angles are complementary. One measures 65 degrees. 2. Two angles are supplementary. One measures 140 degrees. Answer : 25 Answer : 40
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Complementary and Supplementary
Find the missing angle. You do not have a protractor. Use the clues in the pictures. 2. 1. x x 55 165 X=35 X=15
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Interior and Exterior Angles of Triangles
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Sums of Interior Angles
Triangle Quadrilateral Pentagon = 2 triangles = 3 triangles Hexagon Octagon = 4 triangles Heptagon = 5 triangles = 6 triangles
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Convex Polygon # of Sides # of Triangles Sum of Interior Angles Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon 3 1 180 4 2 360 5 3 540 6 4 720 7 5 900 8 6 1080 n n – 2 180•(n – 2)
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Interior Angles 1 2 3 4 5 6 Exterior Angles
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Sums of Exterior Angles
1 2 3 4 5 6 180 180 180•3 = 540 180 Sum of Interior & Exterior Angles = 540 Sum of Interior Angles = 180 Sum of Exterior Angles = 540- 180= 360
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Sums of Exterior Angles
Polygon # of Sides Interior + Exterior Interior Angles Exterior Angles Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 540 180 360 720 360 360 900 540 360 1080 720 360 Sum of Exterior Angles is always 360!
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Angles of Regular Polygons
Sum of the Interior Angles 180(n – 2) Sum of the Exterior Angles Always 360! 180(n – 2) Each Interior Angle n Each Exterior Angle 360 n
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Parallel Lines And Transversals
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Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal. When a transversal t intersects line n and m, eight angles of the following types are formed: Exterior angles Interior angles Consecutive interior angles Alternative exterior angles Alternative interior angles Corresponding angles t m n
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Vertical Angles & Linear Pair
Two angles that are opposite angles. Vertical angles are congruent. 1 4, 2 3, 5 8, 6 7 Supplementary angles that form a line (sum = 180) 1 & 2 , 2 & 4 , 4 &3, 3 & 1, 5 & 6, 6 & 8, 8 & 7, 7 & 5 1 2 3 4 5 6 7 8
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Angles and Parallel Lines
If two parallel lines are cut by a transversal, then the following pairs of angles are congruent. Corresponding angles Alternate interior angles Alternate exterior angles If two parallel lines are cut by a transversal, then the following pairs of angles are supplementary. Consecutive interior angles Consecutive exterior angles Continued…..
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Corresponding Angles & Consecutive Angles
Corresponding Angles: Two angles that occupy corresponding positions. 2 6, 1 5, 3 7, 4 8 1 2 3 4 5 6 7 8
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Consecutive Angles Consecutive Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Consecutive Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. m3 +m5 = 180º, m4 +m6 = 180º 1 2 m1 +m7 = 180º, m2 +m8 = 180º 3 4 5 6 7 8
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Alternate Angles 3 6, 4 5 2 7, 1 8 1 2 3 4 5 6
Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. 3 6, 4 5 2 7, 1 8 1 2 3 4 5 6 7 8
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Example: If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A m<2=80° m<3=100° m<4=80° m<5=100° m<6=80° m<7=100° m<8=80° m<9=100° m<10=80° m<11=100° m<12=80° m<13=100° m<14=80° m<15=100° m<16=80°
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If line AB is parallel to line CD and s is parallel to t, find:
Example: 1. the value of x, if m<3 = 4x + 6 and the m<11 = 126. 2. the value of x, if m<1 = 100 and m<8 = 2x + 10. 3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20. t 16 15 14 13 12 11 10 9 8 7 6 5 3 4 2 1 s D C B A ANSWERS: 1. 30 2. 35 3. 33
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