Question

Given: Measure of arc AB = measure of arc BC,

Measure of angle x = 60°, measure of angle y = 15°
Find: Measure of arc AC

Answer 1

9514 1404 393

Answer:

100°

Explanation:

The relevant relation for angle x is ...

x = (AB +DE)/2

and for angle y, it is ...

y =(AC -DE)/2

Using the second relation to write an expression for DE, we have ...

DE = AC -2y

In the first equation, this lets us write ...

x = (AB +(AC -2y))/2 = (AB +(2AB -2y))/2

2x = 3AB-2y . . . . . . . . . . . . . . multiply by 2

(2x +2y)/3 = AB = AC/2 . . . . . add 2y; divide by 3

AC = (4/3)(x +y) = (4/3)(60° +15°) . . . . multiply by 2, substitute known values

AC = 100°