2D Geometry Questions and Answers

In circle V angle WXZ measures 30 Line segments WV XV ZV and YV are radii of circle V W U X Y What is the measure of WUX in circle V O 60 O 90 O 120 O 150

Line segment GJ is a diameter of circle L Angle K measures 4x 6 H K What is the value of x O 21 24 O 32 044

Line segment XY is tangent to circle Z at point U X T U W Y 12 If the measure of UV is 84 what is the measure of ZYUV A O O O O 42 84 96 168

In circle D angle ADC measures 7x 2 Arc AC measures 8x 8 A B C What is the measure of ZABE O 36 O 43 O 72 O 144

K 70 116 1 What are the measures of JK and ZKIJ Measure of JK Measure of ZKIJ

88 D U 111 A What is the measure of A O 44 O 50 O 64 O 92

40 Q R PR and gs are diameters of circle T What is the measure of SR 50 80 100 120

4 11 Given ZKJL and ZKML intercept arc KL Prove m2KJL mZKML 19 11 rst Co 11 orollary to the Inscribed Angle Theorem K M L Statements 1 ZKJL intercepts KL 2 ZKML intercepts KL 3 mZKJL mKL 4 mZKML mKL 5 mZKJL m KML 1 given 2 given 3 4 5 Reasons

A C B The measure of ZB is 3x 4 and the measure of ZD is 2x 6 What are the measures of angles B and D m2B mZD

R T S The measure of arc QS is 4x 18 What is the value of x O 40 5 O 49 5 O 94 5 O 180

D B A P F O The measure of ADB is 162 What is the measure of ZEAB O

Add Work Question 16 Prove the following identity 1 cos 2y sin 2y degrees 1 cos 2y sin 2y tan y 1

Q 84 R S What is the measure of Qs

58 3 4 2 106 Is the measure of 21 equal to the measure of 22 Why O yes because they intercept the same arc O no because the sides of 22 are longer O no because they intercept the circle at different points

Ground anchor 2 is exactly 58 feet from the base of the tower dashed line in diagram The bottom ground support cable from level 6 to ground anchor 2 is attached to the tower at a height of 142 feet The top ground support cable from level 6 to ground anchor 2 is attached to the tower at a height of 150 feet How long is each support cable to level 6 The bottom cable is SCIEN feet long Round to the nearest hundredth Lesel Lami Support cables Grou aschin

J M P L K The measure of ZKJN is 92 What is the measure of JMK

e is a central angle that cuts off an arc of length s Find the radius of the circle if 8 155 s 5 km O 2 25 km O 1 95 km O 1 85 km 2 15 km O 2 05 km

X Y 86 N What is the measure of ZY O 43 O 68 86 172

haruca a 270 Which of the following shows the correct rotation of parallelogram ABCD OA GOO OB GTS O C

Watch help video In circle F with m EFG 70 and EF Round to the nearest hundredth E F 19 units find the length of arc EG G 4

Yvetia ordered two pizzas for her family Both pizzas are rectangular The larger pizza s width is equal to the length of the smaller pizza and the larger pizza s length is twice the width of the smaller pizza The sum of the perimeters of the two pizzas is 96 inches and the sum of the areas is 288 square inches Determine the dimensions of each pizza Answer The smaller pizza is Number inches by Number inches inches by Number inches and the larger pizza is Number

Evaluate each expression without using a calculator Hint Sketch a right triang tan arc a tan arccos cos arcsin 15 b

Complete the congruence statement M P N H O T U

a as x 2 c as x0 cotx tan x e as x cotx g as x0 csc x i as x cscx k as x 7 secx to complete each state b as x d as x 0 cotx f as x cotx tan x h as x 0 csc x j as x n csc x I as x I 2 7 secx

100 2 Move point C so the measure of arc AC is 50 What is the measure of ZABC 25 D 3 Make a conjecture Which measures will change if you move vertex B of the inscribed angle B A C mZABC 52 mAC 104

Graph g x 2 2 2 given the graph of the parent function f x 2 7 6 5 4 3 2 2 6 5 4 3 2 Me 4 24 3 4 5 V 2 3 5 10

Solve for x Round to the nearest tenth if necessary S 98 R X 31

Explore the properties of inscribed angles by following these steps 1 Move point C so the measure of the inscribed angle ABC is 50 What is the measure of arc AC B A C mZABC 52 mAC 104

9 What is the distance from A to B 12 998 B 59 5 712 R4 000

A 2 B A B Make a conjecture Let points A and B stay in the same position What would happen to the angle formed if the vertex of angle AOB was moved from the center to point C which lies on the circle The measure of angle ACB is measure of angle AOB less than greater than the same as the

20 Plots a few points and then sketch the graph of the polar equation r 5 csc 0 Then convert the equation to rectangular coordinates and confirm your sketch

Compute the sums below Assume that the terms in the first sum are consecutive terms of an arithmetic sequence 9 5 1 363 109 5z 13 0 X S

1 14 ft 2 3 12 ft 1 yd of the shaded area round to the nearest 100ths Area 6 ft 12 ft 7 ft 24 5 ft 7 ft 11 ya A 14 7 24 5 Area Area

Find mZY in rhombus VWXY V 9z 14 mZY Y W 6z 26 X

Look at this diagram P M N 0 K If JL and MO are parallel lines and m JKI 42 what is mLk

a b Find the coordinates of the center of this circle V Center 1 4 What is the radius of the circle radius 6 units C Plot the graph for the given circle

Complete the congruence statement K 20 km 13 km 18 km O 13 km 18 km 20

What values of y and z make ABCD AGHF B 5y 17 C z 28 D F 15z 4y H

tree on a hillside casts a shadow c 210 ft down the hill If the angle of inclination of the hillside is b 19 to the horizontal and the angle of elevation of them a49 find the height of the tree Round your answer to the nearest foot

Plot the graph for the given circle 10 5 10 5 y

16 Determine the length between point A and point B calculate the 1 and 2 in the following graphic 11 16 m 20 00 m DIA T 30 00 m DIA 51 30 m 22 B 5 580 m CLSC Banyago

Consider the circle with two intersecting chords A x 9 D 12 X 6 B

A circle has its center at the origin and a radius of 8 units Draw a graph of this circle 10 10 5

a Consider the circle with equation x 2 y 1 29 State the coordinates of the center of the circle Give your answer in the form a b Center Enter your next step here

The equation of a circle is given by x y 11 Determine the radius of this circle Eston here

etry Q4W3 Float Circles Write the equation for a circle with center 0 0 and radius 6 in the form x h y ur next step here

The equation of a circle is given by x 1 y 4 36 a Find the coordinates of the center of this circle Center Enter your next step here

Write the equation of the circle with its center at 6 1 and a radius of 3 units in the form x h 2 y k r Enter your next step here

18a Consider the circle whose equation is x 2 y 5 9 State the radius ten bera

On the coordinate plane the segment from B 14 11 to C 4 11 forms one side of a rectangle The rectangle has an area of 54 square units Select all of the points that could be a vertex of the rectangle