1) The measure of the central angle is equal to the measure of the intercepting arc.
2) The measure of an inscribed angle is 1/2 the measure of its intercepted arc.
3) x = 43
4) x = 13.8
'Central angle is an angle with its vertex at the center of a circle and with sides that are radii of the circle.'
'An inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle.'
According to the problem,
3) Internal angle = 5x
From the arc-angle relationship we know that the internal angle = 1/2(x°+y°), where x° = 101° and y°= 37°
Therefore, the equation is :
5x = 1/2(101+37)
⇒5x = 1/2(138)
⇒5x = 69
⇒x = 69/5
⇒x = 13.8
4) External angle = 52°
From the arc-angle relationship we know that External angle = 1/2(x°-y°), where x = 190° and y = 2x°
Therefore, the equation will be :
52° = 1/2(190°- 2x°)
⇒52×2 = 190 - 2x
⇒104 = 190 - 2x
⇒2x = 190 - 104
⇒2x = 86
⇒x = 86÷2
⇒x = 43
Hence, we concluded that the value of x in the third problem is 43 and that in the fourth problem is 13.8
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