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TOPICS
Unit-3(Examples)

Example-1 :-  Find measure x in Figure

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

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.

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.

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.

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.

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.

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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