# In Fig. 9.35, AB divides ∠DAC in the ratio 1: 3 and AB =DB. Determine the value of x.

Given,

AB divides DAC in the ratio 1: 3

DAB: BAC = 1: 3

DAC + EAC = 180o

DAC + 108o = 180o

DAC = 180o – 108o

= 72o

DAB = * 72o = 18o

BAC = * 72o = 54o

In

DAB + ADB + ABD = 180o

18o + 18o + ABD = 180o

36o + ABD = 180o

ABD = 180o – 36o

= 144o

ABD + ABC = 180o (Linear pair)

144o + ABC = 180o

ABC = 180o – 144o

= 36o

In

BAC + ABC + ACB = 180o

54o + 36o + x = 180o

90o + x = 180o

x = 180o – 90o

= 90o

Thus, x = 90o

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