Question

What is the arc measure of major arc BAC in degrees?

Answer 1

arc BAC = 276°

Explanation:

the sum of the angles around point D is 360°

sum the central angles and equate to 360

7n + 12 + 6n + 13n - 16 = 360

26n - 4 = 360 ( add 4 to both sides )

26n = 364 ( divide both sides by 26 )

n = 14

Then

∠ ADB = 7n + 12 = 7(14) + 12 = 98 + 12 = 110°

∠ ADC = 13n - 16 = 13(14) - 16 = 182 - 16 = 166°

• the arc of a circle is equal to the central angle it subtends

arc BA = ∠ ADB = 110°

arc AC = ∠ ADC = 166°

Then

arc BAC = arc BA + arc AC = 110° + 166° = 276°