In Fig. `A B||C D` . If `O A=3x-19 ,\ \ O B=x-4` , `O C=x-3` and `O D=4` , find `x` .

In a A B C , D and E are points on the sides A B and A C respectively such that D E// B C If A D=4 , A E=8 , D B=x-4 , and E C=3x-19 , find x .

In Fig. 4.89, if E D C ~ E B A ,\ \ /_B E C=115o and /_E D C=70o . Find /_D E C ,\ \ /_D C E ,\ \ /_E A B ,\ \ /_A E B and /_E B A . (FIGURE)

In Fig. 4.140, /_A B C=90o and B D_|_A C . If A B=5. 7 c m , B D=3. 8\ c m and C D=5. 4 c m , find B C . (FIGURE)

In Figure, lines A B\ a n d\ C D intersect at O . If /_A O C+\ /_B O E=70^0 and \ /_B O D=40^0, find /_B O E and reflex /_C O E

In Fig. 6.13, lines AB and CD intersect at O. If /_A O C\ +/_B O E=70^@ and /_B O D=40^@ , find /_B O E and reflex /_C O E .

In Figure, /_A O B=90^@,\ A C=B C ,\ O A=12\ c m\ a n d\ O C=6. 5 c m . Find the area of /_\A O B .

In a Delta A B C , /_A=x^o,\ \ /_B=(3x-2)^o,\ \ /_C=y^o . Also, /_C-/_B=9^o . Find the three angles.

In Fig. 4.170, A B C D is a trapezium in which A B∥ D C and A B=2\ D C . Determine the ratio of the areas of A O B and C O D . (FIGURE)

A point O inside a rectangle A B C D is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the other pair of triangles. Given: A rectangle A B C D\ a n d\ O is a point inside it. O A ,\ O B ,\ O C\ a n d\ O D have been joined. To Prove: a r\ (A O D)+\ a r\ ( B O C)=\ a r\ ( A O B)+\ a r( C O D)

In Fig, O A ,\ O B are opposite rays and /_A O C+\ /_B O D=90^0, Find /_C O D .