TOPICS
Unit-3(Examples)

Example-1 :-  Find measure x in Figure quadrilateral

Solution :-
   Total measure of all exterior angles = 360° 
   x + 90° + 50° + 110° = 360°       
               x + 250° = 360° 
                      x = 110°
    

Example-2 :-  Find the number of sides of a regular polygon whose each exterior angle has a measure of 45°.

Solution :-
  Total measure of all exterior angles = 360° 
  Measure of each exterior angle = 45°
  Therefore, the number of exterior angles = 360/45 = 8
  The polygon has 8 sides.
    

Example-3 :-  Find the perimeter of the parallelogram PQRS figure parallelogram

Solution :-
  In a parallelogram, the opposite sides have same length. 
  Therefore, PQ = SR = 12 cm and QR = PS = 7 cm
  So, Perimeter = PQ + QR + RS + SP
  = 12 cm + 7 cm + 12 cm + 7 cm 
  = 38 cm 
    

Example-4 :-  In Figure, BEST is a parallelogram. Find the values x, y and z. parallelogram

Solution :-
  S is opposite to B. 
  So, x = 100° (opposite angles property) 
      y = 100° (measure of angle corresponding to ∠x) 
      z = 80° (since ∠y, ∠z is a linear pair) 
    

Example-5 :-  In a parallelogram RING, (Figure) if m∠R = 70°, find all the other angles. parallelogram

Solution :-
  Given m∠R = 70° 
  Then m∠N = 70° because ∠R and ∠N are opposite angles of a parallelogram. 
  Since ∠R and ∠I are supplementary, m∠I = 180° – 70° = 110° 
  Also, m∠G = 110° 
  since ∠G is opposite to ∠I 
  Thus, m∠R = m∠N = 70° and m∠I = m∠G = 110°
    

Example-6 :-  In Figure HELP is a parallelogram. (Lengths are in cms). Given that OE = 4 and HL is 5 more than PE? Find OH. parallelogram

Solution :-
  If OE = 4 then OP also is 4
  So PE = 8, 
  Therefore HL = 8 + 5 = 13
  Hence OH = 1/2 x 13 = 13/2
  × = 6.5 (cms)
    

Example-7 :-  RICE is a rhombus (Figure). Find x, y, z. Justify your findings. rhombus

Solution :-
  x = OE = OI  (diagonals bisect) = 5
  y = OR = OC (diagonals bisect) = 13
  z = side of the rhombus = (all sides are equal ) = 12 
    

Example-8 :-  RENT is a rectangle (Figure). Its diagonals meet at O. Find x, if OR = 2x + 4 and OT = 3x + 1. rectangle

Solution :-
  OT is half of the diagonal TE, OR is half of the diagonal RN. 
  Diagonals are equal here. 
  So, their halves are also equal. 
  Therefore 3x + 1 = 2x + 4 or x = 3
    
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