2D Geometry Questions and Answers

Find the measure of ZC C B 110 m C 30 D

is the centroid of AABC What is the value of x when GD x 4 and GC 4x 5

Applying the Polygon Interior Angle Sum Theorem An internal angle of a regular polygon has a measure of 140 What type of polygon is it 180 n 2 71 and an 180 n 2 180m 360 140m 40m 360 1 The polygon is a nonagon Exterior Angles of Polygons An exterior angle of a polygon is an M of an adjacent side formed by a side of the polygon

7A 15 Quadrilateral ABCD is shown with the given angle measures Select ALL true statements A Angle A measures 140 degrees B The measure of angle A and D must add to 180 degrees C Angle A measures 55 degrees D Angle D measures 55 degrees E Angle D measures 40 degrees B C A 125 40

7A 16 Find the measure of the remaining angles of quadrilateral WXYZ X

13 A fish tank in the shape of a rectangular prism has a base with dimensions of 60 inches by 30 inches and a height of 15 inches If the tank is filled with water to a height of 7 5 inches determine the volume of water in the tank

17A 4 The arc from A to 8 NOT passing through C measures 50 degrees Select ALL the true statements A Angle BCA measures 50 degrees 8 Angle BCA measures 25 degrees C Angle BOA measures 50 degrees D The are from B to C not passing through A measures 180 degrees E Angles CBO and CAO are congruent O A

Polygons Polygons are figures formed from three or more line segments such that each segmentintersects exactly two other one at each endpoint and segments with a common endpoint are collinear concave Convex polygon Every line segment connecting any two points on the polygon itself will consistofno points outside the polygon Concave polygon The extension of at least one side or diagonal contains a point on the inside of the polygon N gon is the number of sides

A circle has a center at 4 1 and a point on the circle is located at 2 5 Write the standard form equation that would graph this circle

11 A rectangular city with dimensions 10 miles by 11 5 miles is surrounded by a circular region of water with a diameter of 15 miles If the city has a population of 445 312 people determine the population density in the city Round your answer to the nearest whole number O a 3 563 b 3 872 2 836 d 2 061

7 The smaller cone is removed from the larger cone Determine the volume of the figure left over when the larger cone is removed from the smaller cone to the nearest tenth 3 6 12 8

6 A granite block in the shape of a right rectangular prism has dimensions 3 centimeters by 4 centim 5 centimters The block has a density of 28 grams per cubic centimeter What is the mass of the block OF a 168 b 1 680 c 16 800 d 168 000 L units for the mass nogsinnl

9 35 of the figure below is filled with sand What is the volume of sand in the lig 2 m 5m 3 m 6 m 7m

Identify and describe concave polygon Analyze the relationship between angle in a triangle and other polygons convex polygon Prove the polygon interior angle and sum theorems Words to Know Fill in this table as you work through the lesson You may also use the glossary to help you a polygon in which the extension of at contains a point the polygon a polygon in which every line segment Calculate angle measures and solve problems with points on the polygon contains and exterior angles one side any two points outside the polygon

Polygon Interior Angle Sum Theorem Polygon interior angle num theorem The sum of the measures of the is 180 n 2 where n is the number of the polygon What is the sum of the measures of the interior angles of a pentagon Apentagon has 5 sides son 5 180 5 2 180 3 angles of any n gon Using the Polygon Interior Angle Sum Theorem What is the measure of K Find the sum of all of the interior angles 1800 2 and n 6 180 4 Find the sum of the angle measures that we know of 720 572 J 106 115 154 90 107 Subtract this from the total measure of all interior angle IM Can be divided into 3 triangles 115 M 106 154 K 107 M

Using the Polygon Interior Angle Sum Theorem Regular polygons are both Find the sum the interior angles 180 n 2 and n 5 180 5 2 180 3 This is a regular polygon so all of the angles will be ofequal measure 540 5 Each interior angle measures 108 REAL WORLD CONNCECTION How can you best describe the cells of a honeycomb using polygons What is the sum of the measures of the interior angles of each cell 180 n 2 180 6 2 180 4 and If the polygon is regular what is the measure M 1000 COPIIIII 1000000O necroo000 CORADD600 P 0

Words to Know exterior angle polygon regular polygon an angle formed by a side in a plane a closed figure formed from three or more line segments such that each segment exactly two other segments one at each endpoint and no segments with a common endpointare a polygon that is both of a figure and an extension of an Angle Measures in Triangles What is the measure of C 180 54 85 A 54 and equilateral 85 B

of water is 1 gram per cm3 An object floats in water if its density is less than water s density and it sinks if its density is greater than water s ass 90 grams is in the shape of a sphere with radius 2 5 centimeters Will the lime sink or float in water Explain or show your reasoning

58 4 A pet supply company makes a small bag that holds 2 pounds of dog food They want to make a bag for large dogs that holds 40 pounds of dog food By approximately what factor will the surface area of the bag increase Round your answer to the nearest tenth

x y 6x 4y 4 0 O Circle 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 N 1 OF 2 3 7 Undo 1 2 3 4 Redo 5 6 x Reset 8 9 10

c sin P Q sin P Q cos Q cos P 2 A satellite s distance above the Earth s surface in km in terms of time in minutes is recorded in the table below 60 232 869 54 48 42 550 869 1000 66 100 24 30 Time min Distance km 6 550 18 12 100 232 36 869 550 232 A number of different equations have been determined and are listed below Equation 1 H t 450 cos 42 550 Equation 3 H t 450 sin t 6 550 a Determine if any of the equations are correct and what error s in the incorrect equations b Determine if other equations can be determined that are not listed already 72 78 232 550 Equation 2 H t 450 cos t 18 550 Equation 4 H t 450 sin t 30 550

5 Use the following image to answer the questions below 60 120 1 m a Based on the picture what properties can you be sure this figure has Think about angles lines and intersectio b Are I and m parallel Explain your thinking What would you need to do to prove that I and mare parallel

is tangent to OW What is XY X Y 20 km 16 km W

The radius of a circle is 6 feet What is the length of a 45 arc 45 r 6 ft

BF is tangent to circle O at point U UA is the circle s diameter Find m FU

3 mA 57 5 m mAB 650 180 A D 5 ft 65 B m B 9 m c 32 5 OD 68 01 7 Area OD 882 5 115

7 Kendon and Success are playing soccer but are trying to see whose soccer ball is better to use with the most air William s soccer ball has a diameter of 22 cm and Daniel s has a 14 cm radius Whose soccer ball is better to use Why

2 Mr Mann s cylindrical fish tank has a base area of 102 cm and a height of 12 cm How much water fish tank hold a 114 cm b 1224 cm c 900 cm d 1020 cm b He d like to wrap his fish tank in clear wrapping to prevent scratches If the diameter is 24 cm how much wrapping will he need

68 11 A circle has a center at 4 1 and a point on the circle is located at 2 5 Write the standard form equation that would graph this circle LT BC Use coordinates to work with objects algebraically x y 14x 12y BC 12 Are the lines below parallel Use mathematics to support your claim 10 NM fo 3 11 PT AT

LI SU Solve pr 50 7 A cylindrical cup is 8 centimeters in height When filled to the very top it holds 480 cubic centimeters of water What is the radius of the cup rounded to the nearest tenth Explain or show your reasoning 50 8 The density of water is 1 gram per cm3 An object floats in water if its density is less than water s density and it sinks if its density is greater than water s Suppose a lime with mass 90 grams is in the shape of a sphere with radius 2 5 centimeters Will the lime sink or float in water Explain or show your reasoning

Pineapple Street intersects Plum Street and Apple Street at their midpoints Your home is at point P You leave your home and jog down Plum Street to Kiwi Street over Kiwi Street to Apple Street up Apple Street to Pineapple Street ove Pineapple Street to Plum Street and then back home up Plum Street How many miles did you jog Apple Street 1 1 miles Pineapple Street 1 3 miles Kiwi Street 2 15 miles Plum Street

Find the length of JM JM G H 12 10 K 15 M N

In the diagram point P is a point of tangency Find the radius r of OO Q 6 P O 18

ABCD is a parallelogram Which statements are true B 22 9x 2 A 110 3y 2 D Oy is greater than 5x O The product of x and y is greater than 100 O x andy are both factors of 80 0 10 times y is less than 9 times x

Find mHK H L 13x mHK MO N J 60 x K

You can calculate the width of the lake using a surveying technique as shown in the diagram Find the width of the lake 115 m W 8 m N 3 X Y 10 m

Find the value of x A D X X 8 E 12 C 6x B

Given AE EC for what value of x is quadrilateral ABCD a parallelogram A B 5x E 2x 1 D C

Which relationship is true for the triangle based on the Law of Sines 18 R O O 110 43 sin 110 18 sin 110 18 sin 110 43 sin 110 43 sin T 43 sin S 43 sin S 18 sin T 18 S 33

Find the value of x Write your answer as a decimal N 29 X O Zo xo Y

A bundle of fabric will cover approximately 1800 square inches Mr Longo wants to cover all the outside surfaces of his rectangular file cabinet with fabric A diagram of the file cabinet is shown below What is the least number of bundles of fabric Mr Longo needs to buy to cover his file cabinet What formula should he use to help him decide a 1 b 2 C 3 d 4 e 5 1111 480 28in 26in 48in

Find the value of x Write your answer as a decimal 122 D A 41 to B

Find the measure of arc RPQ P S 39 O 42 Q The measure of arc RPQ is R degrees

Write an equation of the perpendicular bisector of the segment with the endpoints 3 5 and 9 1 y

Find the measure of ZC Write your answer as a decimal B 100 C A m C 45 D

Find the area of a circle with a diameter of 16 meters Round your answer to the nearest hundredth of a square meter The area of the circle is about square meters

You are planting a garden in the shape of an equilateral triangle as shown in the diagram You want to find the area of the garden to determine how much topsoil you will need 8 ft 60 8 ft 30 A Substitute the values of b and h in the formula A 2 8 ft 2 b h for the area of the garden

Determine the value of x in the diagram 6x X 3x 3x 6x

he mayor wants to build a new gas station so that it is the same distance from the three main roads in town At whi bint of concurrency should the gas station be built O centroid O circumcenter O incenter O orthocenter

Find the value of b Round your answer to the nearest tenth 24 b B 40 20 C