Unit 7 Properties of Quadrilaterals & Polygons

Unit 7: Quadrilaterals & Polygons Review

By Rabah Issa

Interior and Exterior Angles

Use the notes and examples from this week to help answer the following problems. These will be VERY helpful for an upcoming quiz!

Interior Angle Sum

Fill in the Blank

If the sum of interior angles of a polygon is  $$900\degree$$  , how many sides does the polygon have?

Answer: 7 sides

Fill in the Blank

If the sum of the interior angles of a polygon is $$2880\degree$$ , how many sides does the polygon have? 

Exterior Angles

Multiple Choice

Select the correct values for a and m.

• a=50, m=89

• a=50, m=116

• a=105, m=89

• a=105, m=116

Fill in the Blank

What is the value of each exterior angle of a regular 20-gon? ____ $$\degree$$   

Measure of Each Exterior Angle (for regular polygons)

Fill in the Blank

The measure of an exterior angle of a regular polygon is $$45\degree$$  .

Find the number of sides of the polygon. 

Answer: 8 sides

Fill in the Blank

What is the value of x?

*Hint* You need to add the values together and set them equal to the sum of the exterior angles.

Properties of Parallelograms!

• 1) Opposite sides are congruent

• 2) Opposite angles are equal

• 3) Consecutive angles are supplementary

• 4) Diagonals bisect each other

Fill in the Blank

If PQRS is a parallelogram, find the value of x.

*Hint* Remember that in parallelograms, opposites sides are congruent.

Fill in the Blank

If PQRS is a parallelogram, find the value of y.

*Hint* Remember that in parallelograms, consecutive angles are supplementary.

Multiple Choice

Which two figures can always be described as quadrilaterals with all sides congruent?

• square and rhombus
• square and rectangle
• rhombus and parallelogram
• rectangle and parallelogram

Multiple Choice

A trapezoid is a quadrilateral with exactly one pair of _____ sides.

• parallel
• congruent
• perpendicular
• skew

Multiple Choice

In the picture, side AB must be congruent to which side?

• AE
• AD
• CD
• BC

Multiple Choice

What do we know about the diagonals of ALL parallelogram?

• They are congruent
• They bisect each other
• They are perpendicular to each other
• They are parallel to each other

Multiple Choice

Find the missing measure in the parallelogram.

• 75°

• 65°

• 109°

• 35°

Multiple Choice

Find the missing measure in the parallelogram.

• 75°

• 50°

• 65°

• 56°

Multiple Choice

The diagonals of a square are

• parallel
• congruent
• perpendicular
• congruent and perpendicular

Multiple Choice

MNKL is a square. Find the measure of angle MKN.

• 180 degrees

• 90 degrees

• 60 degrees

• 45 degrees

Multiple Choice

What is PN?

• 23

• 46

• 35.5

Multiple Choice

In a square, the diagonals are...

• bisect the angles
• perpendicular
• congruent
• all of the above

Multiple Choice

A Rhombus has congruent  ________

• Angles
• Sides
• Windows
• Doors

Multiple Choice

Which of the following are NOT true about diagonals of a rhombus?

• they are perpendicular
• they bisect each other
• they are congruent

Multiple Choice

Given Rhombus TUVW. Find m∠2.

• 62
• 28
• 90
• 78

Multiple Choice

Given Rhombus TUVW. Find m∠4.

• 62
• 28
• 90
• 78

Multiple Choice

Which of the following statements is false?

• a kite has no parallel sides

• a kite has one pair of congruent angles

• the diagonals of a kite are perpendicular

• the diagonals of a kite are congruent

Multiple Choice

What is x?

• 35
• 45
• 55
• 90

Multiple Choice

Which of the following is NOT a property of a Kite?

• Diagonals are perpendicular to each other.

• One pair of opposite angles are congruent.

• Diagonals bisect each other.

• Two pairs of consecutive sides are congruent.

Multiple Choice

A Trapezoid is a parallelogram.

• True

• False

Multiple Choice

In a Trapezoid, there is exactly ___ pair(s) of parallel sides.

• 1

• 2

• 3

• 4

Multiple Choice

The legs of an isosceles trapezoid are _____.

• parallel
• perpendicular
• congruent
• skew

Multiple Choice

What is the measure of ∠R?

• 65 degrees
• 115 degrees
• 180 degrees
• None of the above

Multiple Choice

What is the measure of ∠P?

• 65 degrees
• 115 degrees
• 180 degrees
• None of the above

Multiple Choice

Find the measure of the indicated angle. 

• 95
• 85
• 35
• 45

Multiple Choice

What is the formula to find the sum of the interior angles of any polygon?

• ^{(n - 2)360}

• 180n

• (n-2)180

• ((n-2)180)/n

• 360/n

Multiple Choice

What is the SUM of the angle measures in a nonagon (9 sides)?

• 1440°
• 900°
• 1080°
• 1260°

Multiple Choice

What is the name of a 7 sided polygon?

• hexagon
• heptagon
• octagon
• nonagon

Multiple Choice

Find the measure of the angle x.

• 105
• 115
• 65
• 75

Multiple Choice

What is the measure of ONE interior angle of a regular octagon?

• 135

• 180

• 145

• 190

Multiple Choice

What is the measure of ONE interior angle in a regular hexagon (6 sides)?

• 60°
• 80°
• 108°
• 120°

Multiple Choice

What is the name of a 7 sided polygon?

• hexagon
• heptagon
• octagon
• nonagon

Multiple Choice

What is the measure of ONE interior angle of a regular octagon?

• 135

• 180

• 145

• 190

Fill in the Blank

For a regular NONAGON, find the measure of one interior angle.

_____ $$\degree$$  

Fill in the Blank

For a regular 15-gon, find the measure of one interior angle.

___ $$\degree$$