Question

In the circle, the measure of angle S = 33 degrees, the measure of arc RS = 120 degrees, and RU is a tangent. The diagram is not drawn to scale.

What is the measure of angle U?

@amistre64
@Hero
@ganeshie8

Answer 1

@mathmale
can you help?

Answer 2

According to my notes

\[m \arc STR = \frac{\angle R}{2}\]

Answer 3

But we are trying to find the angle of U...
If we knew the angle of R, we could just add 33 + R + U = 180
But we don't know R, so... any other ideas?

Answer 4

@SolomonZelman can you help?

Answer 5

But we can find the measure of arc STR right? Why do you ask someone else for help when you haven't even finished consulting with me concerning the issue?

Answer 6

I guess I'm just not understanding sorry. I mean, what's the purpose of finding the measurement of arc STR? How does it help us find U?

Answer 7

Because if you found arc STR. You could find the measure of R, then you would be able to find the measure of U. I don't understand why this is such a mystery to you. Knowing more about the circle is always better is than knowing less.

Answer 8

I gave you the formula to find angle R.

Answer 9

So,
\[240 = \frac{ \angle R }{ 2 }\]
\[480 = \angle R\]
Is that right?

Answer 10

Well, we know that isn't right. I seem to have written the formula incorrectly.

Answer 11

\(\frac{m arc STR}{2} = \angle{R}\)

Answer 12

Oh i think i see the problem. That formula finds the measurement of angle R for the whole circle, not SRT.

Answer 13

Based on that new formula...
\[\frac{ 240 }{ 2 } = \angle R\]
\[120 = \angle R\]

Then,
\[120 + 33 + \angle U = 180\]
\[180 - 153 = \angle U\]
\[\angle U = 27\]

Thanks! Could you help with some more?

Answer 14

A circle with two chords is shown below. The diagram is not drawn to scale.
What is the value of x? Round the answer to the nearest tenth.

Answer 15

If you have two intersecting chords where a + b is the length of one chord and c + d is the length of the other chord, then ab = cd

Answer 16

x = 11.1 :) thanks!