if abcd is a rhombus and if a is 76° find cdb
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Solution:-
Given that ABCD is a rhombus and DAB = 70°
Since, ABCD is a rhombus so
∠ ABC = ∠ CDA
and ∠ DCB = ∠ DAB = 70° .............(1)
And we know that,
∠ DAB + ∠ ABC + ∠ DCB +∠ CDA = 360°
⇒ 70° + ∠ ABC + 70° + ∠ CDA = 360°
∠ ABC + ∠ CDA + 140° = 360°
∠ ABC + ∠ CDA = 360° - 140°
∠ ABC + ∠ CDA = 220°
Since, ∠ ABC = ∠ CDA
So, ∠ ABC + ∠ ABC = 220°
2∠ ABC = 220°
∠ ABC = 110°
Thus,
∠ CDB = 1/2(∠ ABC)
= 1/2(110°)
∠ CDB = 55°
Answer.
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