Please help me out with this TS Math question!!!

[Lazerous]

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I really don't get their explanation.

 

[Lazerous]

The question reads: In the figure, what is the value of angle x.

And the angle on the left is 100 and the one on the right is 140. And the correct answer is B which is 60 degrees.

 

[doc3232]

for starters, vista sucks.

 

[doc3232]

Sorry, I don't see the angles.
There are not two straight lines other than for the angle x.

 

[doc3232]

So the arcs are the angles.
just clicked for me.
So lets say you cut a circle in fourths, then you get 4 90 degree angles. The arcs are 90 degrees and so are the 4 angles at the center.

Here, there is a 140 and a 100
together that is 240. That leaves 120.
this is annoying to explain, verbally much easier.
So 120/2 is 60. The reason we divided by two is because the two lines meet at the other side of the circle RATHER than at the center of the circle. They met around the letter x instead of at the center so hence we divide by two to find the actual angle.
Get it?
As I said, hard to explain.

 

[Lazerous]

Hmmmm....I kind of get it. So had X been at the center of the circle our answer would be 120?

 

[Lazerous]

Also, if X is 60 then that means arc A to C is also 60 right? So that gives us a total of 140+100+60= 300....where are the other 60 degrees to complete the circle then?

 

[PChemGrad]

Remember that the angles of a triangle equal 180 degrees

When ever you have a given angle the opposite angle is 180-x where x is the given angle. Two angles are given.

180 - 100 = 80
180 - 140 = 40
so you have 80 + 40 = 120
so two of the angles inside of the triangle must equal 120 degrees, so to find the missing angle 180 - 120 = 60.
that's where 60 degrees comes from.

 

[klutzy1987]

The easiest way to do this is, the inscribed angle, or the angle formed by two chords meting at a point on the circle is equal to half of the degrees of the arc it forms. In this case the arc is 120 degrees (360-240). Therefore the angle is going to be 60.

 

[Lazerous]

Remember that the angles of a triangle equal 180 degrees

When ever you have a given angle the opposite angle is 180-x where x is the given angle. Two angles are given.

180 - 100 = 80
180 - 140 = 40
so you have 80 + 40 = 120
so two of the angles inside of the triangle must equal 120 degrees, so to find the missing angle 180 - 120 = 60.
that's where 60 degrees comes from.

So are you saying that angle BCA is 80 degrees and angle BAC is 40 degrees?

 

[dentalknight]

...

 

[Streetwolf]

So are you saying that angle BCA is 80 degrees and angle BAC is 40 degrees?

No he's wrong. When you have an angle within a circle such that the vertex of the angle is on the EDGE of the circle, the angle at that vertex is ONE HALF the arc angle value.

When you have an angle within a circle such that the vertex of the angle is the CENTER of the circle, the angle at the vertex is EQUAL TO the arc angle value.

In this case you have 100 and 140 which equals 240. There are 120 degrees left in the arc of the circle (a circle has 360 degrees). Since the vertex of the angle is on the edge of the circle and spans these 120 degrees, the angle itself is 60 (one half of the arc angle). Had the vertex been the center of the circle, then the angle would have been 120.

The other triangle angles are 70 (across from 140) and 50 (across from 100). So yes they still add up to 120 and the last angle is obviously 60.

 

[Ilkaan]

Remember that the angles of a triangle equal 180 degrees

When ever you have a given angle the opposite angle is 180-x where x is the given angle. Two angles are given.

180 - 100 = 80
180 - 140 = 40
so you have 80 + 40 = 120
so two of the angles inside of the triangle must equal 120 degrees, so to find the missing angle 180 - 120 = 60.
that's where 60 degrees comes from.

Like I said I don't think you need to substract from 180. But insteady the value of the angle incribe in the arc is half the value of the arc length so it will be 50+70 =120
180-120 =60
Thank you

 

[klutzy1987]

No he's wrong. When you have an angle within a circle such that the vertex of the angle is on the EDGE of the circle, the angle at that vertex is ONE HALF the arc angle value.

When you have an angle within a circle such that the vertex of the angle is the CENTER of the circle, the angle at the vertex is EQUAL TO the arc angle value.

In this case you have 100 and 140 which equals 240. There are 120 degrees left in the arc of the circle (a circle has 360 degrees). Since the vertex of the angle is on the edge of the circle and spans these 120 degrees, the angle itself is 60 (one half of the arc angle). Had the vertex been the center of the circle, then the angle would have been 120.

The other triangle angles are 70 (across from 140) and 50 (across from 100). So yes they still add up to 120 and the last angle is obviously 60.

You use nicer words than me lol.