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Sagot :

Answer with Step-by-step explanation:

3.) A circle has a full degree of 360.

(x + 150) + (x) = 360

2x = 360 - 150

2x/2 = 210

x = 105

The measures are:

Minor arc: x = 105°

Major arc: (105) + 150 = 165°

4.)  Intersecting Chords of a circle Theorem:

An angle of intersecting chords is equal to the one-half the sum of arcs interecepted by the chords.

Given:

  • Angle of intersecting chord = 90°
  • Arc intercepted: (2x + 24)° and (50x)°

Equation:

90 = (1/2) [(2x + 24) + (50x)]

Find the value of x:

90 = (1/2) (52x + 24)

(90)(2) = 52x + 24    

180 - 24 = 52x

156 = 52x

52x/52 = 156/52

x = 3

Find the measures of intercepted arcs, when x = 3:

  • 2(3) + 24 = 30°
  • 50(3) = 150°

Check:

90 = (1/2) (30 + 150)

90 = (1/2)(180)

90 = 90  (True)