AB is a diameter of circle. C and D are points on the opposite sides of the diameter AB, such that ∠ACD = 25°. E is a point on the minor arc BD, Find the measures of ∠ BED (in degree).
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 115
Given :
AB is a diameter of circle.
C and D are points on the opposite sides of the diameter AB, such that ∠ACD = 25°.
E is a point on the minor arc BD
Calculations :
⇒ ∠ACD = ∠ABD = 25° (angles formed on the same arc)
ADB is the right angled triangle as ∠ADB = 90°
In triangle ADB,
⇒ ∠ADB + ∠ABD + ∠BAD = 180
⇒ 90 + 25 + ∠BAD = 180
⇒ ∠BAD = 180 - (115)
⇒ ∠BAD = 65°
ABED is a cyclic quadtrilateral such that
Sum of the opposite angles of a cyclic quadrilateral is 180°
⇒ ∠BAD + ∠BED = 180
⇒ ∠BED = 180 - 65
⇒ ∠BED = 115°