Question

Geometry help? Medal to best answer!
In TriangleARC, m AngleA = 70°. What is the measure of arc AC?

40°

70°

80°

140°

Answer 1

@eliassaab help?

Answer 2

What do the two segments with length 30 cm tell you about triable ARC?

Answer 3

Im not sure. I have never been good at this geometry stuff. But I think the answer is 80

Answer 4

If a triangle has two sides the same length, what kind of triangle is it? What does that tell you about the other angles in the triangle?

Answer 5

Isosceles Triangle

Answer 6

So the other side has to be the same degree

Answer 7

So it would be 70

Answer 8

You're right so far. What else would you know?

Answer 9

The sides are 30?

Answer 10

You found a second angle of 70, so what would the other angle be?

Answer 11

40

Answer 12

Right. So, you have all three angles of the triangle and you want to find the arc across from angle R. Since the whole circle is 360 degrees and the angles of a triangle total 180 degrees, each arc is twice the measure of the angle across from it on the other side of the circle.

So angle R = 40 and arc AC = 80.

Answer 13

Oh! Pff that makes sense.
Would you mind helping me with 2 other questions, geometry based?

Answer 14

Sure.

Answer 15

Which names a central angle of circle G?

AngleANS

AngleNGL

AngleGSE

AngleGES

Answer 16

GES Is what I think it to be

Answer 17

What do you think they mean by central angle?

Answer 18

I think the angle that comes from the center

Answer 19

That makes sense given the name. More precisely, a central angle of a circle is an angle that has the same center as the center of the circle.

Answer 20

:D Okay
Wait so is it GSE or GES?
Im not sure what the difference is

Answer 21

The center of GSE is S. The center of GES is E.

Which angle has G as the center?

Answer 22

GSE?

Answer 23

Makese more sense

Answer 24

The center of an angle is the middle letter in the name. So _G_.

Answer 25

Rather, _G_ has center of G.

Answer 26

NGL

Answer 27

Exactly.

Answer 28

The only option with G in the middle

Answer 29

Okay!

Answer 30

1 more question, is that oka?

Answer 31

Yup, that's fine.

Answer 32

In circle O, the measure of AngleROW is 110°. What is the measure of arc RAW?

250°

125°

110°

55°

Answer 33

This one I dont know at all

Answer 34

That's okay. There's one fact you need first, then you can use what you know from the first problem.

Answer 35

They give us angle ROW is 110 degrees and we want to find angle RAW. They're both in the same circle, so what part of the circle do they have in common?

Answer 36

R and W

Answer 37

Yes. And in between those points is the arc RW, which is inside both angles.

In the first problem, the arc was twice as large as the angle across from it. In this problem, we have an arc with a central angle (ROW = 110 degrees). How large do you think the arc is compared to that central angle?

Answer 38

It has to be half the size larger

Answer 39

Or almost half

Answer 40

I think its 250

Answer 41

Okay, why is that?

Answer 42

Its more than half and the dot in the middle isnt exactly in the middle.
Im like 99.5% sure its 250

Answer 43

That makes sense. The thing we know from the information about the angle is that the arc RW is 110 degrees, the same as the central angle. The arc RAW takes up the rest of the circle, which is 360 degrees total. So RAW = 360 - RW = 360 - 110 = 250.

Answer 44

And to tie back into the first problem, angle ROW and angle RAW have the same arc of the circle RW.

arc RW = 110
angle ROW = 110
angle RAW = 55

Answer 45

Yeah I think you are right. Okay. Thank you!

Answer 46

No problem.