Angles and Circles

[vampirewitchreine]

I just started this section (I'm nearing the end of my text..... I can't get a clear meaning from reading the section in my text). Anyway, I just want to make sure that my answer is correct. (By the way, this section is Angles and Circles as stated in the na


View attachment 1587
(The figure that I'm working with)

1. measure of Arc QR (50°)
2. measure of Arc PQR (180°?)
3. measure of angle QPR (measure of angle QPR is ½ measure of Arc QR= ½*50= 25°?)
4. measure of Arc PQ (130°?)
5. measure of Arc QPR (310°?)
6. measure of angle PQS (Not entirely sure how to do this one.... I mean, which arc should I use to find the answer?)

 

[vampirewitchreine]

vBulletin Message

Invalid Attachment specified. If you followed a valid link, please notify the administrator
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Hazel, above message is what happens when clicking on your link...
I was so shocked that I drank a tr..trr...trrrriple rye.

Odd..... the attachment came from my computer, so there should be no link......

Here's the image again:

 

[vampirewitchreine]

Odd, cause that's all my book shows me in this section for arcs .


Example from my book:

Find the measure of each arc.
a. Arc PQR
b. Arc PR


Solutions
a. Arc PQR is formed by Arc PR and Arc QR. Use the Arc Addition Postulate.
m Arc PQR = m Arc PR + m Arc QR
m Arc PQR = 100° + 115°
m Arc PQR = 215°

b. Arc PR is the minor arc with the same endpoints as the major arc PQR.
m Arc PR = 360° - m Arc PQR
m Arc PR = 360° - 215°
m Arc PR = 145°

(No, I didn't do that work, the textbook did)

 

[burakaltr]

Odd, cause that's all my book shows me in this section for arcs .


Example from my book:
View attachment 1592
Find the measure of each arc.
a. Arc PQR
b. Arc PR


Solutions
a. Arc PQR is formed by Arc PR and Arc QR. Use the Arc Addition Postulate.
m Arc PQR = m Arc PR + m Arc QR
m Arc PQR = 100° + 115°
m Arc PQR = 215°

b. Arc PR is the minor arc with the same endpoints as the major arc PQR.
m Arc PR = 360° - m Arc PQR
m Arc PR = 360° - 215°
m Arc PR = 145°

(No, I didn't do that work, the textbook did)

As a rule of Thumb, bear in mind that an arc length subtended from the angle having a vertex at the Center of the circle covers the same quantity the angle is. While if we push it back on a point verticed on the circle, then the angle of the vertex would " Halve " !