Mathematics
In Fig. ∠ABC = 69°, ∠ACB = 31°, find ∠BDC.
Circles
3 Likes
Answer
In ∆ ABC,
⇒ ∠ABC + ∠BAC + ∠ACB = 180° (Angle sum property of a triangle)
⇒ 69° + ∠BAC + 31° = 180°
⇒ ∠BAC + 100° = 180°
⇒ ∠BAC = 180° - 100°
⇒ ∠BAC = 80°
We know that,
Angles in the same segment of a circle are equal.
So, ∠BDC = ∠BAC = 80°.
Hence, ∠BDC = 80°.
Answered By
2 Likes
Related Questions
In Fig. A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.
In Fig. ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.
ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is 30°, find ∠BCD. Further, if AB = BC, find ∠ECD.
A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.