Question

in a quadrilateral ABCD the bisectors of angle c and angle d meet at a point e show that a + b equal 2 angle c e d​

Answer 1

Answer:

In quadrilateral ABCD,

∠A+∠B+∠C+∠D=360

o

--- ( 1 ) [ Sum of angles of quadrilateral is 360

o

]

In △CED,

⇒ ∠CED+∠EDC+∠ECD=180

o

[ Sum of angles of triangle is 180

o

. ]

⇒ ∠CED+

2

1

∠D+

2

1

∠C=180

o

⇒ 2∠CED+∠D+∠C=360

o

----- ( 2 )

From ( 1 ) and ( 2 ),

⇒ 2∠CED+∠D+∠C=∠A+∠B+∠C+∠D

⇒ 2∠CED=∠A+∠B

⇒ ∠A+∠B=2∠CED