In the given figure, O is the centre of the circle, AE is the diameter and ∠AOC = 100°.
The value of ∠CDE + ∠CEA is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 90°.
According to the given question,
Given that, ∠AOC = 100°
AE is diameter.
The angle subtende by the chord at the circumference of the circle is half the angle subtended by the chord at the center of the circle.
Now, ∠AOC + ∠COE = 180°
⇒ 100° + ∠COE = 180°
⇒ ∠COE = 80°
Consider chord CE, ∠COE is the angle subtended by the chord at the center and ∠CAE is the angle subtended by the chord at the circumference.
⇒ ∠CDE = ∠COE/2
⇒ ∠CDE = 80°/2
⇒ ∠CDE = 40°
Noe, again consider chord AC, ∠AOC is the angle subtended by the chord at the center and ∠CEA is the angle subtended by the chord at the circumference.
⇒ ∠CEA = ∠AOC/2
⇒ ∠CEA = 100°/2
⇒ ∠CEA = 50°
Now, required sum, ∠CDE + ∠CEA = 40° + 50° = 90°
Hence the value of ∠CDE + ∠CEA is 90°.