Q. 44.0( 8 Votes )

Compute the value of x in each of the following figures:

(i)



(ii)



(iii)



(iv)


Answer :

(i) DAC + BAC = 180o (Linear pair)

120o + BAC = 180o


BAC = 180o – 120o


= 60o


And,


ACD + ACB = 180o


112o + ACB = 180o


ACB = 68o


In ABC,


BAC + ACB + ABC = 180o


60o + 68o + x = 180o


128o + x = 180o


x = 180o – 128o


= 52o


(ii) ABE + ABC = 180o (Linear pair)


120o + ABC = 180o


ABC = 60o


ACD + ACB = 180o (Linear pair)


110o + ACB = 180o


ACB = 70o


In


A + ACB + ABC = 180o


x + 70o + 60o = 180o


x + 130o = 180o


x = 50o


(iii) AB CD and AD cuts them so,


BAE = EDC (Alternate angles)


EDC = 52o


In


EDC + ECD + CEO = 180o


52o + 40o + x = 180o


92o + x = 180o


x = 180o – 92o


= 88o


(iv) Join AC


In


A + B + C = 180o


(35o + 1) + 45o + (50o + 2) = 180o


130o + 1 + 2 = 180o


1 + 2 = 50o


In


1 + 2 + D = 180o


50o + x = 180o


x = 180o – 50o


= 130o


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