Question

if abcd is a rhombus and if a is 76° find cdb

Answer 1

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.