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.
Classification of Angles Acute – less than 90˚ Right – 90˚ Obtuse – greater than 90˚ Straight –180˚
Adjacent Angles When two angles share a common side, they are called adjacent angles. Adjacent angles have the same vertex.
Complementary Angles The sum of the measures of two complementary angles is 90 degrees. To find complement angle, subtract angle measure from 90˚ 4
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 ˚ 5
Linear Pair Angles that are adjacent and supplementary. They share a common side and their sum will be 180˚.
AHSGE 7 Supplementary angles = 180˚ Subtract from 180˚ Answer: C
m<1 and m<2 = 180˚ Let m<2 = x and m<2 =8x Answer: D
Given: <1 and <2 are linear pair If m <1 =49˚,what is m <2 ? a.41˚ b.49˚ c.131˚ d.141˚ 12 Answer: C
AHSGE 10 Supplementary angles = 180˚ Answer: D
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 d.4x Complementary angles = 90˚Answer: A
AHSGE 12 Given: <1 and <2 are complementary. What is the value of x? ? A. 5 B. 10 C D Complementary angles = 90˚ Answer: B
Vertical Angles Formed when two lines or segments intersect. Vertical Angles are congruent, but not adjacent. 13 <1 <2 <4 <3
Perpendicular Lines When two lines intersect at a 90˚ angle, they’re perpendicular. Perpendicular lines always have 90˚ angles. Symbol
Vertical angles are congruent Answer: C
AHSGE 16 Answer: B
Given:m<MPN=(2x+50)˚ m<OPN=(x+35)˚ m<MPO=130˚ What is m<OPN? a.15˚ b.45˚ c.50˚ d.80˚ ●N●N ●M●M ●O●O ●P●P Answer: 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. 19 C A B G
(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 (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
(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 (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
AHSGE 22 Answer: D
AHSGE 23 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 t m n Answer: A
Given: What is ? a.30° b.40° c.50° d.130° 24 Answer: D
Answer: C
Answer: B
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. 27 Hexagon has 6 sides 180(6-2)=(180)(4)=720 Octagon has 8 sides 180( -2)=(180)( )= ( )
AHSGE 28 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° 29 Answer: A
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. 30
AHSGE 31 Answer: D
What is the value of x? a.100° b.80° c.60° d.20° 32 Answer: A