66.9k views
5 votes
PLEASE HELP GEOMETRY ASAP 50 POINTS! REAL ANSWERS ONLY OR WILL BE REPORTED AND DELETED! PLEASE SHOW STEPS!

PLEASE HELP GEOMETRY ASAP 50 POINTS! REAL ANSWERS ONLY OR WILL BE REPORTED AND DELETED-example-1
User JaffParker
by
5.7k points

1 Answer

2 votes

9514 1404 393

Answer:

  • x = 80
  • y = 80

Explanation:

The external angle at A is half the difference of the arcs it intercepts. The inscribed angle y is half the measure of arc CD. The sum of the arcs of a circle is 360°. These relations let us write some equations.

(BC -x°)/2 = ∠A

BC + CD + x° = 360°

y° = CD/2

__

Given that BC = 120° and ∠A = 20°, we can use the first equation to find x.

(120 -x)/2 = 20

120 -x = 40 . . . . . multiply by 2

120 -40 = x = 80 . . . . add x-40

Using known values in the second equation gives ...

120 +CD +80 = 360

CD = 160 . . . . . . . subtract 200

Then y is found from the third equation.

160/2 = y = 80

User Lagina
by
4.9k points