INSCRIBED ANGLES SUBTENDED BY THE SAME ARC OF CIRCLE

Angles subtended by the same arc at the circumference are equal. This means that angles in the same segment are equal

∠ACB = ∠ADB

Both are angles between the arc AB.

Work out the size of each angle marked with a letter. Give reasons for your answers.

Problem 1 :

Solution :

∠BDC = ∠BAC = 25˚ (angles in in the same arc BC)

∠ABC = ∠BCD = 45˚ (angles in the same arc AD)

Problem 2 :

Solution :

∠BAC = 44˚

∠BDC = ∠BAC = 44˚ 

Angle between the same arc BC.

c = 44˚

In triangle BCD.

∠BCD + ∠CDB + ∠DBC = 180

90 + c + d = 180

90 + 44 + d = 180

d = 180 - 134

d = 45

Problem 3 :

Solution :

∠BOC = 2∠BAC

∠BOC = 2∠BDC

∠BAC = ∠BDC

∠BAC = ∠BDC

96 = 2e

e = 96/2

e = 48˚, f = 48˚

Problem 4 :

Solution :

∠BAC = ∠BDC

Reflex of 160 is 200.

g = 1/2(200)

g = 100

h = 100

Problem 5 :

Solution :

h = 18 (h and 18 are angles between the same arc).