Mathematics
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 125°, then ∠BAC is equal to :
35°
40°
45°
55°
Circles
1 Like
Answer
Opposite angles of a cyclic quadrilateral are supplementary.
So,
∠ABC + ∠ADC = 180°
∠ABC = 180° − 125° = 55°.
∠ACB = 90° [Angle in semicircle is a right angle]
In △ABC,
By angle sum property of triangle,
∠BAC + ∠ABC + ∠ACB = 180°
∠BAC + 55° + 90° = 180°
∠BAC = 180° − 145° = 35°.
Hence, option 1 is the correct option.
Answered By
2 Likes
Related Questions
In the given figure, if ∠ACD = 30° and ∠BPD = 100°, then ∠CDB is equal to :
30°
40°
50°
60°
If an arc of a circle subtends a right angle at any point on the remaining part of the circle, then the arc is a :
minor arc
major arc
semi-circle
none of these
In the given figure, if O is the centre of the circle, then the value of x is :
15°
18°
20°
24°
In the given figure, O is the centre of the circle.
If the length of chord AB is equal to the radius of the circle; then ∠ACB is equal to :30°
45°
60°
40°
