Angle Relationships & Parallel Lines

Vocabulary The basics… Acute – Greater than 0°, but less than 90° Right – Exactly 90° Obtuse – Greater than 90°, but less than 180° Straight – Exactly 180° Reflex – Greater than 180°, but less than 360° Full Turn – Exactly 360°

Vocabulary The measure of the angle is the amount of opening between the sides of the angle. Vertex – Point where rays meet. Ray (side of angle)

Vocabulary Adjacent angles are “side by side” and share a common ray. 15º 45º

These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

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

Transversal Transversal – A line that intersects two or more lines. n Line n is a transversal.

Angles X and Angle Y are complementary and add up to 90 °. Complementary Angles Complementary Angles – Two angles that add up to 90° Angles X and Angle Y are complementary and add up to 90 °. X Y

Complementary Angles but not Adjacent 30º 40º 50º 60º Adjacent and Complementary Angles Complementary Angles but not Adjacent

Angles X and Angle Y are supplementary and add up to 180 °. Supplementary Angles Supplementary angles - Two angles that add up to 180° Angles X and Angle Y are supplementary and add up to 180 °. X Y

Supplementary Angles Adjacent and Supplementary Angles 40º 140º 120º 60º Adjacent and Supplementary Angles Supplementary Angles but not Adjacent

Vertical Angles Vertical Angles - A pair of opposite angles formed by the intersection of two lines. Vertical angles are always equal. A Angle A and Angle B are vertical angles. They are equal! B

Vertical Angles A and C are vertical! B and D are vertical! B C A

Corresponding Angles Corresponding angles – Two congruent angles that lie on the same side of the transversal. A and B are corresponding angles. A B Line n is a transversal. n

Alternate Interior Angles A =  C B =  D They are alternate interior angles. (Interior = Inside!) A B D C n Line n is a transversal.

Alternate Exterior Angles A =  C B =  D They are alternate exterior angles. (Exterior = Outside!) A B D C n Line n is a transversal.

Properties of Parallel Lines Name the… Corresponding Angles Vertical Angles Supplementary Angles Alternate Interior Angles Alternate Exterior Angles A & E, B & F, C & G, D & H A & D, B & C, F & G, E & H A & B, B & D, D & C, etc… C & F, D & E A & H, B & G A B C D E F G H

Try this… Find the missing angle. x° 36° 90 – 36 = 54°

Try this… Solve for x. 3x° 2x° 3x + 2x = 90° 5x = 90 x = 18

Try this… Solve for x. 2x + 5 + x + 25 = 90° 3x + 30 = 90 3x = 60

Try this… Solve for x. x 138° 180 – 138 = 42°

Try this… Solve for x. 4x 5x 4x + 5x = 180 9x = 180 x = 20

Try this… Solve for x. 2x + 10 + 3x + 20 = 180 5x + 30 = 180 5x = 150

Try this… Find the missing angles. A = 138° D = 42° B = 138° E = 138° C D E G F A = 138° B = 138° C = 42° D = 42° E = 138° F = 138° G = 42°

Try this… Find the missing angles. 70 + 70 + b = 180 40 + 65 + d = 180 70 ° 70 ° b° 40 ° Hint: The 3 angles in a triangle sum to 180°. d ° 65 ° 70 + 70 + b = 180 140 + b = 180 b = 40° 40 + 65 + d = 180 105 + d = 180 d = 75°