Q. 43.9( 20 Votes )

# In each of the figure given below, AB||CD. Find the value of x in each case.(i)(ii) (iii)

(i) x = 100

Given AB||CD, ABE = 35° and EDC = 65°

Draw a line PEQ||AB or CD

1 = ABE = 35°[AB||PQ and alternate angle] _______________ (i)

2 = EDC = 65°[CD||PQ and alternate angle] _______________ (ii)

From equations (i) and (ii)

1 + 2 = 100°

x = 100°

(ii) x=280

Given AB||CD, ABE = 35° and EDC = 65°

Draw a line POQ||AB or CD

1 = ABO = 55°[AB||PQ and alternate angle] _______________ (i)

2 = CDO = 25°[CD||PQ and alternate angle] _______________ (ii)

From equations (i) and (ii)

1 + 2 = 80°

Now,

BOD + DOB = 360°

80° + = 360°

x = 280°

(iii) x=120

Given AB||CD, BAE = 116° and DCE = 124°

Draw a line EF||AB or CD

BAE + PAE = 180° [Because PAB is a straight line]

116° + 3 = 180°

3 = 180° - 116°

3 = 64°

Therefore,

1 = 3 = 64° [Alternate angles] ____________________ (i)

Similarly, 4 = 180° - 124°

4 = 56°

Therefore,

2 = 4 = 56° [Alternate angles] ____________________ (ii)

From equations (i) and (ii)

1 + 2 = 64° + 56°

x = 120°

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