Mathematics
AC is diameter, AE is parallel to BC and ∠BAC = 50°.
Statement (1) : ∠EDC + 50° = 180°.
Statement (2) : ∠EDC + ∠EAC = 180°.
Both statements are true.
Both statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Circles
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Answer
It is given that AC is diameter and angles in a semicircle is a right angle.
⇒ ∠ABC = 90°
Since, AE is parallel to BC and AB is transversal.
⇒ ∠ABC + ∠BAE = 180° [The sum of co-interior angles formed when a transversal intersects two parallel lines is always 180°]
⇒ 90° + ∠BAE = 180°
⇒ ∠BAE = 180° - 90°
⇒ ∠BAE = 90°
⇒ ∠BAC + ∠EAC = 90°
⇒ 50° + ∠EAC = 90°
⇒ ∠EAC = 90° - 50°
⇒ ∠EAC = 40°
AEDC form a cyclic quadrilateral and sum of either pair of opposite angles of a cyclic quadrilateral is 180°.
⇒ ∠EDC + ∠EAC = 180°
⇒ ∠EDC + 40° = 180°
So, statement 1 is false but statement 2 is true.
Hence, option 4 is the correct option.
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