# Compute the value of x in each of the following figures:(i)(ii)(iii)(iv)

(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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