Question

Find the value of unknown angles ​

Answer 1

$\huge\boxed{\mathcal\red{Answer:}}$

∠ABC + ∠BAC + ∠BCA = 180° (Sum of three angles is 180°)

x° + x° + 40° = 180°

2x° + 40° = 180°

2x° = 180° - 40°

x° = 140°/2

x° = 70°

∠ABC + ∠DBC = 180° (By Linear Pair)

x° + y° = 180°

70° + y° = 180°

y° = 180° - 70°

y° = 110°

∠BAC = 70°

∠ABC = 70°

∠DBC = 110°

Answer 2

∠B=40°

Rhombus is also a parallelogram. Hence the opposite angle are equal.

∴∠D=∠B=40°

Further is a parallelogram,

ad jaunt angles add upto 180 °

$$\Rightarrow \angle A +\angle B =180^o\Rightarrow \angle A+40^o=180^o\Rightarrow\angle A =180^o-40^o=140^O$$

opposite angles are equal , hence ∠A=∠C=140°

Thus all angles are as shown below:

∠A=140 ° ,∠B=40 ° ,∠C=140 ° ,∠D=40°