Question

what is the measure of arc YZ, Given that measure of angle xyz in a circle is 32 degrees

Answer 1

Do you know that angle X is an inscribed angle?

Answer 2

It is called an inscribed angle because its vertex is on the circle. What does your theorem about inscribed angles say?

Answer 3

I do not know

Answer 4

Look in your book.

Answer 5

f an angle is incribed in a circle, then the subtended arc angle is twice the angle.

This theorem is true whether the angle is acute or obtuse.

Answer 6

Do you know what that says?

Answer 7

no i don't understand

Answer 8

An inscribed angle is half of its arc.

Answer 9

So how big is the arc?

Answer 10

The arc is 64 degrees

Answer 11

Bingo

Answer 12

i also have another question

Answer 13

what is the measure of angle bcd

Answer 14

sorry angle BDC not BCD

Answer 15

I assume that is angle D?

Answer 16

yes....

Answer 17

When 2 secants intersect outside a circle, the angle is half the difference of the intercepted arcs.

Answer 18

So basically i substract 42 from 15

Answer 19

No. subtract 15 from 42 and divide the answer by 2

Answer 20

ok thanks!

Answer 21

yw