Angles subtended by the same arc at the circumference are equal. This means that angles in the same segment are equal
∠ACB = ∠ADB
Problem 1 :
Find the value of x.
Solution :
∠ADB = ∠ACB (angle between the same arc AB)
So, x = 18
Problem 2 :
Solution :
∠ADB = ∠ACB (angle between the same arc AB)
So, x = 27
Problem 3 :
Solution :
∠ADB = ∠ACB (angle between the same arc AB)
So, x = 55
Problem 4 :
Solution :
x + 12˚ + 91˚ = 180˚
x = 180˚ - (12˚ + 91˚)
x = 180˚ - 103˚
x = 77˚
Problem 5 :
Solution :
x + 29˚ + 101˚ = 180˚
x = 180˚ - (29˚ + 101˚)
x = 180˚ - 130˚
x = 50˚
Work out the size of each angle marked with a letter. Give reasons for your answers.
Problem 6 :
Solution :
a = 25 and b = 45
Because angles in the same arc.
Problem 7 :
Solution :
c = 44 (angle in the same arc CD)
∠DCB = 90
In triangle DCB,
∠DCB + ∠CDB + ∠DBC = 180
90 + d + c = 180
90 + d + 44 = 180
134 + d = 180
d = 180 - 134
d = 46
Problem 8 :
Solution :
∠DOC = 96
∠DOC = 2e
96 = 2e
e = 96 / 2
e = 48
f = 48
Angle in the same arc.
Problem 9 :
Solution :
Reflex of angle DOC = 360 - 160 ==> 200
Reflex of angle DOC ==> 2g = 200
g = 100
h = 100
Angle in the same arc.
Problem 10 :
D is the point on the circumference of the circle such that angle BDC = 60
i) Write down the size of angle CAB
ii) Work out the size of angle ACB.
Solution :
∠BDC = 60, then ∠BAC = 60
In triangle ABC,
∠BAC + ∠ABC + ∠ACB = 180
60 + 90 + ∠ACB = 180
150 + ∠ACB = 180
∠ACB = 180 - 150
∠ACB = 30
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM