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)
