In Fig, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.
ΔABC,
∠ABC = ∠ACB + ∠BAC = 180° 6
9 + 31 + ∠BAC = 180
100 + ∠BAC = 180
∠BAC = 180 – 100
∠BAC = 80°
∠BAC and ∠BDC are angles in same segment. These are equal.
∠BDC = ∠BAC = 80°
∴ ∠BDC = 80°
In Fig. 9.23, A,B and C are three points on a circle with centre O such that ∠ BOC = 30° and ∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.
In Fig. 9.26, 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.