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Angles and Plane Figures Questions

1.  The sum of angles of a triangle is given by the expression (2a+b)0 while that of a quadrilateral is given by Image From EcoleBooks.com. Calculate the values of a and b     (4 mks)

2.  The figure below represents a quadrilateral ABCD. Triangle ABX is an equilateral triangle. If Image From EcoleBooks.com, find Image From EcoleBooks.com with Image From EcoleBooks.com   (2 mks)

 

 

 

3.  Wanjiku is standing at a point P, 160m south of a hill H on a level ground. From point P she observes the angle of elevation of the top of the hill to be 670

(a) Calculate the height of the hill  (3 mks)

(b) After walking 420m due east to the point Q, Wanjiku proceeds to point R due east of Q, where the angle of elevation of the top of the hill is 350. Calculate the angle of elevation of the top of the hill from Q     (3 mks)

(c) Calculate the distance from P to R    (4 mks)

4.  In the triangle XYZ below, find the angle ZXY. (3mks)

Image From EcoleBooks.com

5.  The exterior angle of a regular polygon is equal to one-third of the interior angle. Calculate the number of sides of the polygon and give its name. (4 mks)

6.  In the figure below, lines AB and LM are parallel.

 

 

ecolebooks.com

 

 

Find the values of the angles marked x, y and z  (3 mks)

7.  From points A and B on a level ground the angles of elevation to the top of the building are 240 and 380 respectively. If the distance between A and B is 47m and that of B from the foot of the building is X;

(a) Form an expression for the height of the building

(b) Calculate the height of the building

(c) Find the difference in the distance between the top of the building and points A and B

8.  The angle of elevation of the top of the tower from the foot of a building is 63.510. The angle of depression of the top of the building from the op of the tower is 18.430. The building and the tower are 30m apart. Find

  1. The height of the tower   (1mk)
  2. The height of the building (2mks)

9.  The exterior angle of a regular polygon is an eighth of the interior angle. How many sides does the regular polygon have?  (3 marks)

10.  The sides of a parallelogram are 4cm by 5cm and its area is 12cm2. Calculate its angles.  (3 marks)

11.  From a point 20m away on a level ground the angle of elevation to the lower window line is 270 and the angle of elevation to the top line of the window is 320. Calculate the height of the window.

 (3 marks)

12.  A regular polygon has its exterior angle 180, and one of its sides 16cm. calculate its area.

(to 2 d.p) (3mks)

13.  The angle of depression of a point A on the ground from the top of a post is 180 and that of  another point B on the same line as A nearer to the foot of the post is 250. If A and B are 70m  apart,

 (a) Draw a sketch to represent positions of A and B. (2mks)

 (b) Using your sketch calculate

 (i) The height of the post from the ground level (ans 1 d.p) (6mks)

 (ii) The distance of point A from the foot of the post. (2mks)

14.  The figure below shows an irregular polygon PQRSTUVW.

Calculate the sum of all the interior angles in the figure below.

Image From EcoleBooks.com

 

 

 

 

 

 

 

 

 

 

 

 

 

 

15.  The angles of elevation from two points A and B to the top of a storey building are 480 and 570 respectively. If AB = 50m and the point A and B are opposite each other; Calculate;

a) the distance of point A to the building  (2 mks)

b) the height of the building (2 mks)

 

Angles and Plane figures Answers

1

Image From EcoleBooks.com

Image From EcoleBooks.com

Image From EcoleBooks.com

 

M1

 

M1

 

 

M1

A1

 

formation of the equations

attempt to solve

2

Image From EcoleBooks.com

Image From EcoleBooks.com

B1

B1

 

3

 

Image From EcoleBooks.com

 

h = 160 × tan 670

= 376.94m

 

 

Image From EcoleBooks.com

Image From EcoleBooks.com

 

Tan ө = Image From EcoleBooks.com

 

 

 

 

 

 

 

 

 

 

 

Image From EcoleBooks.com

 

 

 

 

 

 

 

 

 

Image From EcoleBooks.com

 

 

 

M1

 

 

 

 

 

M1

 

A1

 

 

 

 

 

 

 

 

 

M1

 

 

 

 

 

M1

A1

 

 

 

 

 

 

M1

 

M1

 

 

 

 

 

 

 

M1

 

A1

4.

aA2 = b2 + c2 – 2bc cos A

42 = 32 + 62 – 2 x 3 x 6 cos

-29 = -36cos

-29 = cos

-36

36.340=

 

M1

 

M1

 

A1

 

Substitution

 

Attempt to simplify

  

03

 

5.

Image From EcoleBooks.com

The polygon is an octagon

M1

 

 

M1

 

A1

3

6.

Image From EcoleBooks.com

B1

B1

B1

3

9.  Let the ex < be x0 ALT

 In < 8x0  n
= No. of sides

n – 2 180 = 8 360 M1M1

 x + 8x = 180…………..  M1   n n

 x = 20 n = 18 sides A1

 

 No of sides = 360 M1

20

= 18 sides A1

 

3

10.    

 

5 h

 

B

4

 

Area = 5 x sin  = 12  M1

 = 36.870 A1

B = 143.130 A1

3

 

11.50 270

Window x  

 

    h

 

 

 Tan 270 = h

20  M1

h = 10.19m

 Tan 320 = x/20  M1

x = 12.50m

 Window height = 2.31m A1

 

3

12.

3600 = 180

n

n = 3600
= 20 sides

180

Area = ( ½ x 16 x 16/2 tan 810) x 20

= (8 x8 x 6.3138) x 20

= 8081.66cm2

 

 

B1

 

M1

 

A1

 
  

03

 

13.

(a)

Image From EcoleBooks.com

Sketch

(b) i)

h = tan250
 h = x tan 25

x

h = tan180
 h = tan 18(x + 70)

x+70

equating the two equations

x tan 250 = x tan 180 + 70 tan 180

x(tan 25 tan 180) = 70 tan 180

x = 70 tan 180

tan250 – tan180

x = 22.744 = 160.8

0.1414

h = 160.8tan 25 = 75m

(c) Distance of A to the front of post

= x + 70

= 160.8 + 70

= 230.8m

 

B2

 

 

 

 

M1

 

M1

 

 

M1

 

M1

 

M1

 

A1

 

B1

 

 

M1

 

A1

 
  

10

 

 

14.

 

{2(8) – 2} x 90

 

14 x 90

 

12600

 

M1

 

 

A1

2

 

15.

Image From EcoleBooks.com

Image From EcoleBooks.com

 

 

 

 

 

 

 

 

M1

 

 

A1

 

 

M1

 

 

A1

 
  

04

 

 

 

 

 

 

 

 

 

 

 

 

 


 




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