Find the measure of angle and indicated arc.
Problem 1 :
Solution :
In a cyclic quadrilateral, the opposite angles are supplementary.
∠FGH = 180 - 119 ==> 61
∠FGH = (1/2) Measure of arc (VH + FV) ---(1)
∠GFV = 180 - 65 ==> 115
∠GFV = (1/2) Measure of arc (GH + VH) ---(2)
From (2)
115 = (1/2) (168 + measure of arc VH)
230 = 168 + measure of arc VH
Measure of arc VH = 230 - 168
Measure of arc VH = 62
By applying this value in (1)
61= (1/2) (62 + measure of arc FV)
122 - 62 = measure of arc FV
Measure of arc FV = 60
Problem 2 :
Solution :
In a cyclic quadrilateral, the opposite angles are supplementary.
∠KRQ = 180 - 110 ==> 70
∠KRQ = (1/2) (measure of arc PQ + KP)
70 = (1/2) (30x + 50)
140 = 30x + 50
140 - 50 = 30x
30x = 90
x = 3
Problem 3 :
Find the values of x, y and z.
Solution :
∠DAB + ∠DCB = 180
∠DAB + z = 180 ---(1)
∠DAB = (1/2) measure of arc BD
∠DAB = (1/2) 136
∠DAB = 68
Applying the value of ∠DAB in (1), we get
z = 180 - 68
z = 112
∠ADC + ∠ABC = 180
x + y = 180
∠ADC = (1/2) Measure of arc AC
∠ADC = (1/2) 180
∠ADC = 90 = x
x = 90
Applying the value of x in x + y = 180, we get
90 + y = 180
y = 180 - 90
y = 90
Problem 4 :
Find the values of x, y and z.
Solution :
x = (1/2) (106 + 58)
x = (1/2) (164)
x = 82
y = 180 - 82 (Opposite angles are supplementary)
y = 98
z = 180 - 93
z = 87
Problem 5 :
Find measure of angles A, B, C and D.
Solution :
∠BAD = (1/2) Measure of BD
∠BAD = (1/2) (115 + 86)
∠BAD = 100.5
∠BCD = 180 - 100.5
∠BCD = 79.5
∠ADC = (1/2)(54 + 115)
∠ADC = (1/2)(169)
∠ADC = 84.5
∠ABC = 180 - 84.5
∠ABC = 95.5
Problem 6 :
Solution :
x = (1/2)(64 + 122)
x = (1/2)(186)
x = 93
y = 180 - 83
y = 97
Problem 7 :
Find ∠DBC, ∠ACD
Solution :
∠DBC = (1/2)ABC Measure of arc DC
∠DBC = (1/2)96
∠DBC = 48
∠ACD = (1/2)ABC Measure of arc AD
∠ACD = (1/2)90
∠ACD = 45
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May 21, 24 08:51 AM
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