Question

AC is diameter, AE is parallel to BC and ∠BAC = 50°.

Statement (1): ∠EDC + 50^{\circ} = 180°

Statement (2): ∠EDC + ∠EAC}= 180°

विकल्प

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is false, and statement 2 is true.

Explanation: 

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.