LINES, TRIANGLES AND POLYGON

 

PROBLEM 1

 

 

 

 

 

 

In the figure above, find x in terms of a, b and c (U.M.E 1981, Question 17)

 

SOLUTION

 

 

 

 

 

 

 

 

 

PROBLEM 2

 

 

 

 

 

 

 

 

PQ is parallel to RS, calculate the value of x(U.M.E 1981,Question 40)

 

SOLUTION

 

 

 

 

 

 

 

 

 

PROBLEM 3

 

 

 

 

 

 

 

 

 

 

The angles marked in the figures above are measured in degrees, find x (U.M.E 1980, Question 45)

 

SOLUTION

	S

 

PROBLEM 4  

 

 

 

 

 

 

 

SOLUTION

 

 

 

 

 

 

 

PROBLEM 5

 

 

 

 

 

 

 

 

 

      

 

PROBLEM 6

 

 

 

 

 

 

The above figure FGHK is a rhombus. What is the value of angle x (U.M.E       1983, Question 19)

 

SOLUTION

 

PROBLEM 7

 

 

 

 

 

 

In the figure above PQR is a straight line, find the value of x and y (U.M.E 1983, Question 44)

 

 

PROBLEM 8

 

 

 

 

 

 

 

 

 

SOLUTION

 

 

PROBLEM 9

 

 

 

 

 

 

 

In the figure above, find angle x (U.M.E.1985, Question 49)

 

SOLUTION

 

 

 

 

 

 

 

 

PROBLEM 10

 

 

 

 

 

 

 

 

 

           

 

PROBLEM 11

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PROBLEM 12

 

 

 

 

 

 

 

 

In the figure above, find the value of X (U.M.E. 1987, Question 36)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PROBLEM 13

 

 

 

 

 

 

 

 

 

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

 

PROBLEM 14

 

 

 

 

 

 

 

 

 

PROBLEM 15

For which of the following angles is a regular polygon possible (i) 35 (ii) 18  (iii) 15 (U.M.E 1988 Question 32)

 

 

PROBLEM 16

 

 

 

 

 

 

 

 

 

 

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

 

SOLUTION

 

PROBLEM 18

 

 

 

 

 

 

 

SOLUTION

 

 

 

 

 

PROBLEM 19

 

 

 

 

 

 

 

 

 

 

PROBLEM 20

                                                                       

 

 

 

 

 

 

 

 

In the diagram above, calculate the value of x   (U.M.E 2005, Question 18)

 

SOLUTION

                       

 

 

 

 

 

PROBLEM 21

 

 

 

 

 

 

 

 

 

In the diagram above, find the value of x

 

 

 

 

 

 

 

 

 

 

 

 

SOLUTION

 

Alternative method

 

 

 

 

 

 

 

 

 

 

 

 

PROBLEM 22

 

 

 

 

 

 

 

 

 

In the figure above, find the value of x (U.M.E 1991, Question 30)

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

 

 

 

PROBLEM 25

 

 

 

 

 

 

 

In the figure above, find the value of y (U.M.E 1991, Question 37)

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

PROBLEM 26

                                                                                                           

 

 

 

 

 

SOLUTION                                                                                                                                                                                                   

 

 

 

 

 

 

 

PROBLEM 27

 

PROBLEM 28

 

 

 

 

 

 

 

If in the diagram above, FG is parallel to KM, find the value of x

 

SOLUTION                                                                                                                                                                                                                                                                                                                                                                           

 

 

 

 

 

 

 

PROBLEM 29                                                                                                                                                                                                                                                                                                                      

 

 

 

 

 

 

 

 

 

 

SOLUTION

Each side of the pentagon will have 108^o  

 

 

 

 

 

 

 

 

 

 

 

PROBLEM 30

A regular polygon has 150^o as the size of each interior angle.  How many sides has the polygon. (U.M.E 1993, Question 26)

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

 

PROBLEM 31

 

 

 

 

 

 

 

 

 

 

SOLUTION                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       

 

 

 

 

 

 

 

 

PROBLEM 32

 

 

 

 

 

 

 

 

 

 

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

 

 

PROBLEM 34

 

 

 

 

 

 

 

 

 

 

In the diagram above K,M, and N are parallel lines, what is the value of the angle marked x  (U.M.E 1995, Question 32)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          

Note: I have re-labelled the given diagram.

 

 

 

 

 

 

 

PROBLEM 35

 

 

 

 

 

 

 

 

SOLUTION

 

 

 

 

 

 

 

 

 

 

PROBLEM 36

In a regular polygon, each interior angle double its corresponding exterior. Find the number of sides of the polygon (U.M.E 2000, Question 23)

 

 

SOLUTION

 

 

 

 

 

 

 

 

PROBLEM 37

 

 

 

 

 

 

 

 

SOLUTION

 

 

 

 

 

 

Question 38

 

 

 

 

 

 

 

 

 

 

 

In the diagram above . The size of angle marked x is (a) 100^o   (b)                   80^o   (c)  50^o   (d)  30^o    (UME 2008, Question 25 set U03, type A)

 

SOLUTION

 

 

 

 

 

 

 

 

                                                                              

 

                                                            

               

Answer: Option B

 

Problem 39

Find the exterior angle of 12 sided regular polygon (a)  12^o  (b)  24^o  (c) 25^o   (d)  30^o  ((UME 2008, Question 26 set U03, type A)

 

Solution

Sum of exterior angles =360^o

For 12 sided regular polygon

            12x =360^o

                x = 30^o

Answer: Option D

 

 

 

Problem 40

 

 

 

 

 

 

 

 

 

In the figure  and XY = TY, , find angle marked n (a) 47^o  (b) 52^o (c)  56^o  (d)  99^o (UME 2009, Question 26 set U03)

 

Solution

 

 

 

 

           

 

 

 

 

                     

Answer: Option B