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Question

In the given figure, AD bisects ∠BAC in the ratio 1 : 3 and AD = DB. Determine the value of x.
Figure

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Solution

In the figure,

BAC+108°=180° [Linear pair ]BAC=72°

Now, divide 72° in the ratio 1 : 3.
a+3a=72°a=18°a=18° and 3a=54°
Hence, the angles are 18o and 54o.
BAD=18° and DAC=54°

Given,
AD=DBDAB=DBA=18°

In ABC, we have:
BAC+ABC+ACB=180° angle sum property72°+18°+x°=180°x°=90°Therefore, x = 90

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