ABCD is a rhombus if angle DAB=70 degree , then find angle CDB - Maths - Quadrilaterals

Question

ABCD is a rhombus if angle DAB=70 degree , then find angle
CDB

Priyanka Kedia · Accepted Answer

Given, ABCD is a rhombus and $∠ D A B = 70^{0}$

Since, ABCD is a rhombus.So

$∠ A B C = ∠ C D A a n d ∠ D C B = ∠ D A B = 70^{0} ...... (1)$

And we know that,

$∠ D A B + ∠ A B C + ∠ D C B + ∠ C D A = 360^{0} \Rightarrow 70^{0} + ∠ A B C + 70^{0} + ∠ C D A = 360^{0} \Rightarrow ∠ A B C + ∠ C D A = 360^{0} - 140^{0} = 220^{0} \Rightarrow ∠ A B C + ∠ C D A = 220^{0} \Rightarrow ∠ A B C + ∠ A B C = 220^{0} \Rightarrow {2 ∠ A B C = 220}^{0} \Rightarrow ∠ A B C = 110^{0}$

Thus,

$∠ C D B = \frac{1}{2} (∠ A B C) = \frac{1}{2} (110^{0}) = 55^{0} \Rightarrow ∠ C D B = 55^{0}$

ABCD is a rhombus if angle DAB=70 degree , then find angle CDB.