What is inscribed angle ?
Angle whose vertex is on the circle ang whose sides are chords of a circle.
Intercepted arc ?
The arc that lies between two chords on the inscribed angle.
Measure of an inscribed angle is half of its intercepted arc.
Find the measure of angle indicated.
Problem 1 :
Find ∠G
Solution :
∠HGF = 1/2 arc HF
∠HGF = (1/2) 90
∠HGF = 45
Problem 2 :
Solution :
∠RTS = 1/2 arc RS
∠RTS = (1/2) 48
∠RTS = 24
Problem 3 :
Solution :
∠ABC = 1/2 arc AC
51 = (1/2) x
x = 51(2)
x = 102
Problem 4 :
Find measure of arc TV.
Solution :
∠TUV = 1/2 arc TV
38 = 1/2 arc TV
measure of arc TV = 2(38)
measure of arc TV = 76
Problem 5 :
Find measure of arc RS and m∠STR. What do you notice about m∠STR and m∠RUS.
Solution :
m∠RUS lies between chords SU and RU.
m∠RUS = 1/2 of measure of arc RS
31 = 1/2 of measure of arc RS ----(1)
m∠RTS lies between chords ST and RT.
m∠RTS = 1/2 of measure of arc RS
Applying the value of 1/2 of measure of arc RS in (1), we get
m∠RTS = 31
m∠RTS and m∠RUS are equal.
Problem 6 :
Find the following.
Solution :
∠ZYW = angle between ZY and YW
∠ZXW = angle between ZX and XW
∠ZYW = (1/2) measure of arc ZW
72 = (1/2) measure of arc ZW
Measure of arc ZW = 72(2)
Measure of arc ZW = 144
∠ZXW = (1/2) measure of arc ZW
∠ZXW = (1/2) 144
∠ZXW = 72
Problem 7 :
Find the values of x and y.
Solution :
∠ABD = ∠ACD (lies between the same arc AD)
x = 58
∠CDB = ∠BAC (lies between the same arc BC).
y = 41
Problem 8 :
Find ∠BAC
Solution :
∠BAC = (1/2) measure of arc CD
∠BAC = (1/2) (80)
∠BAC = 40
Problem 9 :
Solution :
In the triangle BDC,
∠B + ∠D + ∠C = 180
∠B + 49 + 70 = 180
∠B = 180 - 119
∠B = 61
∠DBC = (1/2) of measure of arc DC
61 = (1/2) of measure of arc DC
Measure of arc DC = 61(2) ==> 132.
Problem 10 :
Solution :
∠RSQ = 1/2 measure of arc QR
95 = 1/2 measure of arc QR
Measures of arc QR = 95(2)
Measures of arc QR = 190
Measure of arc QR + Measure of arc RS + Measure of arc SQ = 360
190 + 75 + Measure of arc SQ = 360
Measure of arc SQ = 360 - 190 - 75
Measure of arc SQ = 95
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM