In a quadrilateral ABCD, E is a point in the interior of the quadrilateral such that DE and CE are the bisector of ∠D and ∠C, respectively. If ∠B = 82º and ∠DEC = 80º, then ∠A = ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 78º
Let ∠EDC and ∠ECD be 'a' and 'b'.
In EDC,
a + b + 80 = 180
a + b = 100.
2a + 2b = 200.
We know that the sum of all the angles of a quadrilateral will be equal to 360°.
∠A + ∠B + ∠C + ∠D = 360.
∠A = 360 - 82 - 200 = 78°.