Mathematics
In the adjoining figure, BD= AD = AC. If ∠ABD = 36°, find the value of x.
Triangles
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Answer
From figure,
∠ABD = ∠BAD = 36° (As angles opposite to equal sides are equal.)
∠BDA = 180° - (36° + 36°) = 180° - 72° = 108°.
From figure,
∠BDA + ∠ADC = 180°
108° + ∠ADC = 180°
∠ADC = 72°.
In △ADC,
As AD = AC,
∴ ∠ADC = ∠ACD = 72° (As angles opposite to equal sides are equal.)
∠ADC + ∠ACD + ∠DAC = 180°
72° + 72° + ∠DAC = 180°
∠DAC = 180° - 144° = 36°.
From figure,
∠BAD + ∠DAC + x = 180°
36° + 36° + x = 180°
72° + x = 180°
x = 108°.
Hence, x = 108°.
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