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)

Answer :

(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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