Mathematics
ABCD is a rhombus. If ∠BCA = 35°, find ∠ADC.
Quadrilaterals
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Answer
In rhombus ABCD, all sides are equal:
AB = BC = CD = DA
Thus, alternate angles are equal:
∠DAC = ∠BCA
It is given that ∠BCA = 35°.
⇒ ∠DAC = ∠BCA = 35°
And, ∠DAC = ∠ACD [as AD = CD]
⇒ 35° = ∠ACD
In triangle ADC, sum of all the angles of triangles is 180°
⇒ ∠DAC + ∠ACD + ∠ADC = 180°
⇒ 35° + 35° + ∠ADC = 180°
⇒ 70° + ∠ADC = 180°
⇒ ∠ADC = 180° - 70°
⇒ ∠ADC = 110°
Hence, the value of ∠ADC is 110°.
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