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Unit-3(Examples)

Understanding Quadrilaterals

**Example-1 :-** Find measure x in Figure

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^{°}.

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

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.

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.

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.

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.

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.

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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