In the given figure D, E, and F are the feet of the perpendiculars from the vertices A, B, and C, respectively, of a triangle ABC. If angle BED and angle BFE (in degrees) is 24° and 110°, respectively, what is the measure (in degrees) of angle EBF?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 46.
Taking BC as the diameter, a circle is drawn.
Here, ∠BEC = 90°.
Considering EC a chord, ∠EBC = ∠EFC = 20°
Considering AB as the diameter, an6other circle is drawn.
Here, ∠AEB is a subtended angle on circumference from the diameter which is 90°.
Now, considering the chord BD, ∠BED = ∠BAD = 24°
So, in ΔABD,
∠BAD + ∠ADB + ∠ABD = 180°
⇒ 24° + 90° + ∠ABE + ∠EBD = 180°
⇒ 24° + 90° + ∠ABE + 20° = 180°
⇒ ∠ABE = 46°
⇒ ∠EBF = 46°