Question

What is the value of x in the figure below?
A. 20°
B. 40°
C. 80°
D. 160°

Answer 1

Sorry. Is the arc \(80^o\))?

Answer 2

I was assuming it was to be honest.

Answer 3

What do you notice?

Answer 4

I see that the top angle, O, is labeled 80 degrees & it forms a triangle.

Answer 5

Yes, do you notice what kind of triangle is that?

Answer 6

Two equal sides?

Answer 7

Ahhh, isosceles, right?

Answer 8

Correct.

Answer 9

So 2 angles at the bottom are equal. Next, you calculate it?

Answer 10

Okay, how exactly would I calculate it on this? Would I divide?

Answer 11

Sum of angles in a triangle is 180. And one of them is 80, so sum of the other two angle is... And they are equal so...

Answer 12

Hm, then I don't think my answer would be here because if you add the sum of the 2 angles with 80 on these answer choices, none of them equal to 180.

Answer 13

So as you can see, the two bottom angles are \(50^o\). Moreover, sum of one of them plus x is 90.

Answer 14

I see, so what would that mean? I'm in a panic, lol

Answer 15

So you understand why each angle at the bottom is \(50^o\), right?

Answer 16

Yes, I do. They are both equal, & added to 80, equal 180.

Answer 17

Right.

Answer 18

So, is there another step in this then?

Answer 19

Yes, as you can see, one of the radius is perpendicular to the given line.

Answer 20

This is a property of the tangent of a circle, right?

Answer 21

Yes, you are right. :)

Answer 22

So the answer is ...