Solving for x and y
Answers:
First Circle:
On a whole circle, the measure of it is 360. If the other arc measures 210, then we must compute it to find the measure of the other arc.
Let n be the other arc.
n + 210 = 360
n = 360 - 210
n = 150
The variable x is a central angle of the circle and its intercepted arc is equal to 150°.
Central Angle (x) = Intercepted Arc (n)
Central Angle (x) = 150°
x = 150°
Second Circle:
Let n be the missing arc.
n + 115 + 95 = 360°
n + 210 = 360°
n = 360 - 210
n = 150
The variable x is an inscribed angle of the circle, and its intercepted arc is equal to 150.
Inscribed Angle (x) = [tex]\frac{1}{2}[/tex] Intercepted Arc (n)
Inscribed Angle (x) = [tex]\frac{1}{2}[/tex] 150
Inscribed Angle (x) = 75
x = 75°
Third Circle:
Let n be the other arc.
n + 250 = 360
n = 360 - 250
n = 110°
The variable x is an inscribed angle of the circle, and n is its intercepted arc that is equal to 110.
x = [tex]\frac{1}{2}[/tex] n
x = [tex]\frac{1}{2}[/tex] (110)
x = 55°
The intercepted arc of inscribed angle y is equal to 250°.
Let m be the intercepted arc of inscribed angle y.
y = [tex]\frac{1}{2}[/tex] m
y = [tex]\frac{1}{2}[/tex] (250)
y = 125°
Fourth Circle:
Let n be the missing arc.
n + 250 + 50 = 360
n + 300 = 360
n = 360 - 300
n = 60
Variable x is an angle formed by a tangent line and a secant line.
x = [tex]\frac{1}{2}[/tex] ( Major arc - Minor Arc)
x = [tex]\frac{1}{2}[/tex] ( 250 - 60)
x = [tex]\frac{1}{2}[/tex] (190)
x = 95°
Fifth Circle:
Variable x is the angle formed by intersecting two secants.
x = [tex]\frac{1}{2}[/tex] (Major arc - Minor Arc)
x = [tex]\frac{1}{2}[/tex] (105 - 25)
x = [tex]\frac{1}{2}[/tex] (80)
x = 40°
Sixth Circle:
x = [tex]\frac{1}{2}[/tex] (Major Arc + Minor Arc)
x = [tex]\frac{1}{2}[/tex] ( 135 + 55)
x = [tex]\frac{1}{2}[/tex] (190)
x = 95°
