Question

Please help with the two files below. Will give brainliest and 20 points. 10 points for each question.

Answer 1

Answer:

1. x = 108°
2. ∠BAC = 54°

Step-by-step explanation:

There are a couple of angle relations that apply to these problems.

• the measure of an arc is the same as the measure of the central angle it subtends
• the angle where chords cross is the average of the two arcs subtended.

1.

The measure of arc BC is given as 108°. The measure of central angle BXC is the same:

  x = 108°

2.

Angle BAC is the average of arcs BC and DF:

  (BC +DF)/2 = BAC

  ((12x +15) +(9x -12))/2 = (10x +4)

Multiplying by 2 and collecting terms gives ...

  21x +3 = 20x +8

  x = 5 . . . . . . . . . . subtract 20x+3

∠BAC = 10x +4 = 10(5) +4

∠BAC = 54°