Question

ABCD is a quadrilateral . AO and BO are the bisectors of angle A and B which meet at O . If angle c is 70 and angle d is 50 find angle AOB

Answer 1

The above is an explanation of the answer in brief.If you have any queries please ask.

Answer 2

$\fbox{\underline\purple{Given~:}}$

∠C = 70° , ∠D = 50°

$\fbox{\underline\orange{To~Find~:}}$

We have to find ∠AOB .

$\fbox{\underline\green{Solution~:}}$

Let ∠A and ∠B = ϰ .

We know that sum of all sides of Quadrilateral is 360° .

$x + x + 70° + 50° = 360°$

$2x + 120° = 360°$

$2x = 360° - 120°$

$2x = 240°$

$x = \frac{240°}{2}$

$x = 120°$

In ∠AOB

∠A = 60° , ∠B = 60°

Let , ∠O = ϰ

We know that sum of all sides in a Triangle is 180° .

$∠A + ∠B + ∠O = 180°$

$60° + 60° + x = 180°$

$120° + x = 180°$

$x = 180° - 120°$

$x = 60°$

⠀⠀⠀⠀ ⠀⠀$\fbox{\underline\red{x = 60°~Ans.}}$