Question

The bisectors of ∠B and ∠C of quadrilateral ABCD meet at a point R inside the quadrilateral.If ∠A=95 and ∠D=111 , find ∠BRC

Answer 1

Given,

Bisectors of ∠B and ∠C meets at point R,

∠A = 95° and ∠D = 111°,

and a Quadrilateral ABCD

To find,  

The angle of ∠BRC

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Now,

In Quadrilateral ABCD,  

A!=95°  

D!=111°

A! + D! = 111° + 95° = 206°

B! + C! = 360°  − 206°  = 154°

In ΔABC,

(BRC)! + (RBC)! + (BCR)! =180°

(BRC)! + $\frac{1}{2}$ (B!+C!) = 180°  

(BRC)! +  (154) = 180°  

(BRC)! = 180°  − 77°

(BRC)! = 103°  

∴(BRC)! = 103°

(This will be considered the value of ∠BRC in the quadrilateral ABCD which meets at a point R inside the quadrilateral)

Hence the value of ∠BRC is 103°.