Question

ABCD is a rhombus if E and F lie on AD and CD respectively such that ED = FC and AF÷BE = 1 then the sum of measure of angle BED and angle AFD equals to (1) 90° (2)180° (3)270° (4) 150°

Answer 1

In triangle ABE and triangle AFD

BE = AF
Angle BAE = Angle ADF
and

Angle ABE = Angle AFD


Thus triangle ABE and AFD are similiar

Thus Angle AEB = Angle EAF

In triangle AEO

Angle AEB +  Angle EAO + Angle AOE = 180

Thus Angle AEB = 45 deg

thus Angle DEO + Angle DFA = 2 * 135

                                                 = 270 deg

thus the answer is

(3)