In a quadrilateral ABCD, the bisector of ∠C and ∠D meet at point E. If ∠CED = 57ᵒ and ∠A = 47ᵒ, then the measure of ∠B is:

In a quadrilateral ABCD, the bisector of ∠C and ∠D meet at…

In a quadrilateral ABCD, the bisector of ∠C and ∠D meet at point E. If ∠CED = 57^o and ∠A = 47^o, then the measure of ∠B is:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 67^o

In Quadrilateral ABCD,

∠A+∠B+∠C+∠D = 360

now, triangle CED

∠CDE +∠ECD +∠CED = 180

(∠C+∠D)/2 + ∠CED =180

(∠C+∠D)/2 + 57 = 180

(∠C+∠D)/2 =123

∠C+∠D = 246

then, ∠A+∠B + 246 = 360

47+∠B+246 = 360

∠B = 360-293 = 67