Math, asked by sarvagnasreegeethika, 1 month ago

ABCD is a quadrilateral the bisectors of angle A and angle B intersect at P show that angle C+angle D=2 angle APB

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Answered by purisamika
0

Answer:

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If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, bisectors of ∠B and ∠C at Q, bisectors of ∠C and ∠D at R and bisectors of ∠D and ∠A at S, then PQRS is a

Answer

Correct option is

D

quadrilateral whose opposite angles are supplementary

From question the diagram we get is above.

From figure,

∠QPS=∠APB      (Vertically opposite angles) ----  (1)

Consider, △APB  

∠APB+  

2

1

​  

∠A+  

2

1

​  

∠B=180  

 

∠APB=180  

−  

2

1

​  

(∠A+∠B)  -----  (2)

From equation (1) & (2),

∠QPS=180  

−  

2

1

​  

(∠A+∠B)  -----  (3)

Similarly, ∠QRS=180  

 -  

2

1

​  

(∠C+∠D)  ---- (4)

From (3) &(4),

∠QPS+∠QRS=360  

 -  

2

1

​  

(∠A+∠B+∠C+∠D)

                          =360  

−  

2

1

​  

(360  

)

                          =360  

−180  

 

∴ ∠QPS + ∠QRS  = 180  

 

Hence, PQRS is a quadrilateral whose opposite angles are supplementary.

Step-by-step explanation:

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