VII-I Apply Properties of Angles & Relationships

Between Angles

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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˚

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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 ˚

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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˚

1 2

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 – 4xb. 180 – 4xc. 4x + 180d. 4x + 90

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Complementary angles = 90˚ Answer: A

AHSGE 12

Given: <1 and <2 are complementary.

What is the value of x?

?

A. 5B. 10C. 12.5D.

21.25 Complementary angles = 90˚

Answer: B

Vertical Angles

Formed when two lines or segments intersect.

Vertical Angles are congruent, but not adjacent.

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<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

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

●M ●O

●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.

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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 8.

1 23 456

7 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.

3 45

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(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.

3 45

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(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.

1 2

78

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. <8b. <7c. <6d. <3

t

m

n

1 2

3 4

7 8

5 6

Answer: A

Given: What is ?

a. 30°b. 40°c. 50°d. 130°

m n,m150m2

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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.

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Hexagon has 6 sides180(6-2)=(180)(4)=720

Octagon has 8 sides180( -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°

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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.

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AHSGE 31

Answer: D

What is the value of x?

a. 100°b. 80°c. 60°d. 20°

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Answer: A