Mathematics

In the figure (2) given below, BC = CD. Find ∠ACB.

Triangles

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Answer

From figure,

∠DAC = 180° - 138° = 42°.

∠BDC = 180° - ∠ADC = 180° - 116° = 64°.

In △BCD,

∠CBD = ∠BDC = 64°.

∠DCB = 180° - (∠CBD + ∠BDC) = 180° - (64° + 64°)

= 180° - 128° = 52°.

In △ADC,

∠DCA = 180° - (∠CAD + ∠ADC) = 180° - (42° + 116°)

= 180° - 158° = 22°.

From figure,

∠ACB = ∠DCB + ∠DCA = 52° + 22° = 74°.

Hence, ∠ACB = 74°.

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