Mathematics
Assertion (A): In the figure, ∠ACB = 70°.
Reason (R): Opposite angles of a cyclic quadrilateral are equal.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Answer
In triangle ABD,
∠DAB = 60°
∠DBA = 50°
From figure,
⇒ ∠DAB + ∠DBA + ∠ADB = 180° [Angle sum property of a triangle]
⇒ 60° + 50° + ∠ADB = 180°
⇒ 110° + ∠ADB = 180°
⇒ ∠ADB = 180° - 110°
⇒ ∠ADB = 70°
Angle in same segment are equal.
∠ADB = ∠ACB = 70°
So, assertion (A) is true.
We know that,
In cyclic quadrilateral opposite angles are supplementary (sum = 180°), not equal.
So, reason (R) is false.
A is true, R is false.
Hence, option 1 is the correct option.
Related Questions
ABCD is a cyclic quadrilateral. If ∠BAD = (2x + 5)° and ∠BCD = (x + 10)°, then x is equal to :
65°
45°
55°
5°
Assertion (A): In the given figure, if O is the centre of the circle, then ∠ACB = 40°.
Reason (R): Angle at the centre is double the angle at the remaining part of the circle.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Assertion (A): In the figure, if AB is a diameter of the circle, then ∠BAC = 50°.
Reason (R): Sum of two angles of a cyclic quadrilateral is always 180°.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
Assertion (A): In the figure, if O is the centre of the circle, then ∠BCD = 80°.
Reason (R): Exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
