Answer:
13. x=11; MN=65°; NP=115°; NQP=245°
15. x=9; AD=108°; BC=23°; DC=139°; DBC=221°
Step-by-step explanation:
13.
The marked arcs are congruent, so we can equate the given expressions for their measures:
10x -45 = 6x -1
4x = 44 . . . . . . . . . add 45-6x
x = 11 . . . . . . . . . . divide by 4
The arc measures are found by using the value of x in the corresponding expression. Arcs around a circle total 360°.
arc MN = (10(11) -45)° = 65°
arc NP = 180° -65° = 115°
arc NQP = 360° -NP = 245°
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15.
The sum of arcs around a circle is 360°. We can use this fact to write an equation involving the given expressions. Clockwise from A, we have ...
90 +(2x +5) +(17x -14) +12x = 360
31x = 279 . . . . . . . subtract 81, collect terms
x = 9 . . . . . . . . . divide by 31
The arc measures are found by using the value of x in the corresponding expression.
arc AD = 12(9)° = 108°
arc BC = (2(9) +5)° = 23°
arc DC = (17(9) -14)° = 139°
arc DBC = 360° -DC = 221°
