VII-I Apply Properties of Angles & Relationships Between Angles

1. VII-I Apply Properties of Angles & Relationships Between Angles 1 Standard VII: The student will be able to solve problems involving a variety of algebraic and geometric concepts.

2. Classification of Angles Acute – less than 90˚ Right – 90˚ Obtuse – greater than 90˚ Straight –180˚

3. Adjacent Angles When two angles share a common side, they are called adjacent angles. Adjacent angles have the same vertex.

4. Complementary Angles • The sum of the measures of two complementary angles is 90 degrees. • To find complement angle, subtract angle measure from 90˚

5. Supplementary Angles • The sum of the measures of two supplementary angles is 180 degrees. • If two angles form a straight line (angle), the sum of their measures is 180 degrees. • Supplementary angles may be adjacent, but do not need to be. • To find supplement angle, subtract angle measure from 180 ˚

6. Linear Pair Angles that are adjacent and supplementary. They share a common side and their sum will be 180˚.

7. Supplementary angles = 180˚ Subtract from 180˚ Answer: C AHSGE

8. Answer: D m<1 and m<2 = 180˚ Let m<2 = x and m<2 =8x

9. Given: <1 and <2 are linear pair If m <1 =49˚,what is m <2 ? 41˚ 49˚ 131˚ 141˚ 1 2 Answer: C

10. Answer: D Supplementary angles = 180˚ AHSGE

11. The measure of an angle in degrees is 4x. Which of these represents the measure of its complement? a. 90 – 4x b. 180 – 4x c. 4x + 180 d. 4x + 90 Complementary angles = 90˚ Answer: A

12. ? Given: <1 and <2 are complementary. What is the value of x? 5 10 12.5 21.25 Answer: B Complementary angles = 90˚ AHSGE

13. Vertical Angles Formed when two lines or segments intersect. Vertical Angles are congruent, but not adjacent. <1 <2 <4 <3

14. Perpendicular Lines When two lines intersect at a 90˚ angle, they’re perpendicular. Perpendicular lines always have 90˚ angles. Symbol

15. Answer: C Vertical angles are congruent

16. Answer: B AHSGE

17. Answer: B

18. Given: m<MPN=(2x+50)˚ m<OPN=(x+35)˚ m<MPO=130˚ What is m<OPN? 15˚ 45˚ 50˚ 80˚ ●N ●M ●O ●P Answer: C

19. B G A C Transversals • If two parallel lines are cut by a transversal, alternate interior angles are congruent, corresponding angles are congruent, and same side interior angles are supplementary. • Parallel Lines – Two lines in a plane that never meet. The symbol || means “Parallel To.” Line AB || Line CG.

20. 1 2 3 4 5 6 7 8 3 4 5 6 (Corresponding Angles) – If two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent.  1 and  5,  2 and  6,  3 and  7,  4 and  8. (Alternate Interior) – If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. 3 and 6, and 4 and 5.

21. 1 3 2 4 5 6 7 8 (Same Side Interior Angle) – If two parallel lines are cut by a transversal, then each pair of same side interior angles is supplementary. 3 and 5, 4 and 6. (Alternate Exterior Angle) – If two parallel lines are cut by a transversal, then each pair of alternate exterior angles is congruent. 1 and 8, 2 and 7.

22. Answer: D AHSGE

23. t 1 2 m 3 4 5 6 n 7 8 Answer: A If line m is parallel to line n, which of the angles has the same measure as <1? a. <8 b. <7 c. <6 d. <3 AHSGE

24. Given: What is ? a. 30° b. 40° c. 50° d. 130° Answer: D

25. Answer: C

26. Answer: B

27. Convex Polygons • The sum of the measures of the interior angles of a convex polygon is 180(n-2), where n is the number of sides of the polygon. Octagon has 8 sides 180( -2)=(180)( )= ( ) Hexagon has 6 sides 180(6-2)=(180)(4)=720

28. Answer: A AHSGE

29. Answer: A A convex polygon has 12 sides. What is the sum of the measures of the interior angles? a. 1800° b. 1980° c. 2160° d. 2520°

30. Interior Angles • The sum of the measures of the interior angles of a triangle is 180 degrees. • Exterior Angle is equal to sum of the measure of its remote (opposite) interior angles.

31. Answer: D AHSGE

32. Answer: A What is the value of x? a. 100° b. 80° c. 60° d. 20°