Everything Maths Grade 10

Q

R S

T

y

34 ◦

x 41 ◦

b)Find the value ofy.

c)Find the value ofx.

7. a)QuadrilateralXW V Uwith sidesXW ∥U VandXU∥W Vis given. Also given isX^=yand
   V^= 36◦;XU W^ = 102◦andWU V^ =x. Prove thatXW V Uis a parallelogram.

X

W V

U

y

36 ◦

102 ◦ x

b)Determine the value ofy.

c)Determine the value ofx.

8.In parallelogramADBC, the bisectors of the angles(A; D; B; C)have been constructed, indicated with
the red lines below. You are also givenAD=CB,DB=AC,AD∥CB,DB∥AC,A^=B^and
D^=C^.
Prove that the quadrilateralM N OPis a parallelogram.
Note the diagram is drawn to scale.

A

B

C

D

1

2

1

2

1

2

2

1

a

c

b

d

2

M 1

1 2

N

2

O 1

2 1

P

Chapter 12. Euclidean geometry 407