Question

determine the measure of XZ

Answer 1

@Mertsj @phi @zepdrix @Jonask

Answer 2

@JamesJ @Mimi_x3

Answer 3

@jim_thompson5910

Answer 4

@jim_thompson5910 @JamesJ

Answer 5

@JamesJ help please?

Answer 6

@Jonask

Answer 7

I'm honestly not sure about how to do this. I'll be curious to see how one arrives at the answer.

Answer 8

@JamesJ Oh okay no worries! Let's see who can help me out :)

Answer 9

use the formula found on this page

http://www.mathwarehouse.com/geometry/circle/tangents-secants-arcs-angles.php

look at the first formula (Formula I)

Answer 10

Hi @jim_thompson5910 ! so you subtract? :)

Answer 11

then divide by 2

Answer 12

ok, so call the answer x. Then
(185 - x)/2 = 76

Now solve for x

Answer 13

so if p was the measure of arc XZ, then

(m arc ST - m arc XZ)/2 = angle ZYX

(185 - p)/2 = 76

solve for p

Answer 14

so 76 - 185 @jim_thompson5910

Answer 15

(185 - p)/2 = 76

185 - p = 76*2

keep going to solve for p

Answer 16

I got 109

Answer 17

then do I do 76 x 2?

Answer 18

(185 - p)/2 = 76

185 - p = 76*2

185 - p = 152

keep going to solve for p

Answer 19

109 is wrong. Check your work. Follow jim's equations above.

So we have reduced the problem to
185 - p = 76*2 = 152

Answer 20

okay so now do I do 185 - 152 ?

Answer 21

I got 33

Answer 22

better

Answer 23

p = measure of arc XZ

so because p = 33, we can say

measure of arc XZ = 33 degrees

Answer 24

Okay great thank you!!

Answer 25

you're welcome