In a quadrilateral ABCD - A -150 degree- B - C - D - Find B - C - D

Sum of all angles of quadrilateral is equal to 360 degree Therefore, A+B+C+D = 360 ⇒ 150 + B +C+D = 360 As B= C = D 150 + 3B = 360 B = 70 degree =C = D ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Sum of Exterior Angles in a Polygon

In a quadrila...

Question

In a quadrilateralABCD, $∠ A = 150^{\circ}$ , $∠ B = ∠ C = ∠ D .$ Find angle $B, C, D .$

Open in App

Solution

Given: $∠ A = 150^{\circ}$
We know that sum of all angles of quadrilateral is equal to $360^{\circ}$
Therefore, $∠ A + ∠ B + ∠ C + ∠ D = 360^{\circ}$
$\Rightarrow 150^{\circ} + ∠ B + ∠ C + ∠ D = 360^{\circ}$
$\Rightarrow 150 + 3 ∠ B = 360^{\circ}$ [As $∠ B = ∠ C = ∠ D$ ]
$\Rightarrow 3 ∠ B = 360^{\circ} - 150^{\circ}$
$\Rightarrow ∠ B = \frac{210}{3}$
$∴ ∠ B = ∠ C = ∠ D = 70^{\circ}$

Suggest Corrections

Similar questions

Q. In a quadrilateral ABCD,

∠ A + ∠ C = 180^{\circ}

then

∠ B + ∠ D =

Q. In a quadrilateral ABCD,

∠ A = 30^{\circ}, ∠ B = 150^{\circ}, ∠ C = 30^{\circ} and

∠ D = 150^{\circ}

Then ABCD is a

Q. In quadrilateral ABCD,

∠ B = 90^{0}, ∠ C - ∠ D = 60^{0}

and

∠ A - ∠ C - ∠ D = 10^{0}

, Find

∠ A, ∠ C, ∠ D

Q. In quadrilateral ABCD

∠

= 90^{o}

∠

- ∠

= 60^{o}

and

∠

- ∠

- ∠

= 10^{o}

. Find

∠

∠

C and

∠

Q. In a quadrilateral

A B C D

∠ D = 90^{o}

∠ A = ∠ B = ∠ C

, find

∠ A

Join BYJU'S Learning Program

In a quadrilateralABCD, ∠A=150∘, ∠B=∠C=∠D.Find angle B,C,D.

Given: ∠A=150∘We know that sum of all angles of quadrilateral is equal to 360∘ Therefore,∠A+∠B+∠C+∠D=360∘⇒150∘+∠B+∠C+∠D=360∘⇒150+3∠B=360∘ [As ∠B=∠C=∠D]⇒3∠B=360∘−150∘⇒∠B=2103∴∠B=∠C=∠D=70∘

In a quadrilateralABCD, $∠ A = 150^{\circ}$ , $∠ B = ∠ C = ∠ D .$ Find angle $B, C, D .$