Question

20 points and brainliest to the best correct answer, do and show work for numbers 13 and 15. Questions are in the photo, thank you.

Answer 1

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°