Mathematics
In the figure (1) given below, AB = AD, BC = DC. Find ∠ABC.
Triangles
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Answer
Join BD.
In △ABD,
AB = AD
∴ ∠ABD = ∠ADB = a.
∠ABD + ∠ADB + ∠DAB = 180°
a + a + 54 = 180°
2a + 54° = 180°
2a = 126°
a = 63°.
In △BCD,
BC = CD
∴ ∠CDB = ∠DBC = b.
∠CDB + ∠DBC + ∠BCD = 180°
b + b + 116° = 180°
2b + 116° = 180°
2b = 64°
b = 32°.
From figure,
∠ABC = a + b = 63 + 32 = 95°.
Hence, ∠ABC = 95°.
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