d

Question

d

mathmate · Answer

All of them can be solved using the fact that the tangent to a circle is perpendicular (at 90 degrees) to the radius joining the point of tangency.

mathmate · Answer

Start with #6.
What is the sum of interior angles of a quadrilateral?

mathmate · Answer

Good, you know the value of how many of the interior angles?

mathmate · Answer

Look at the diagram.
One is indicated in numbers, one is indicated by a symbol, two are indicated by the fact that they are tangents.
Add them together and equate the sum to 360, solve for x.

mathmate · Answer

Look at the diagram.

One is indicated in numbers, (60 degrees)
one is indicated by a symbol,  (x)
two are indicated by the fact that they are tangents (means 90 degrees)
Add them together  (60+x+90+90)
and equate the sum to 360, 
            60+x+90+90=360
Now your job:  solve for x.

mathmate · Answer

Find x from the following equation:
60+x+90+90=360
If you leave out the right hand side, you won't get the answer.

mathmate · Answer

Exactly! Good job!
Now you can try the other problems in a similar way!

mathmate · Answer

For
60+x+90+90=360
I would proceed as follows:
x+90+90+60=360
x+240=360
Subtract 240 from both sides
x+240-240=360-240
x+0 = 120
x=120

mathmate · Answer

What is 60?

mathmate · Answer

what is 600?

mathmate · Answer

Remember this time you are working with a triangle.
What is the sum of interior angles of a triangle?

mathmate · Answer

Right!

mathmate · Answer

How many tangents are there?

mathmate · Answer

So can you rewrite your equation?  You have put 90 degrees two times.

mathmate · Answer

Perfect!
Now you can try the last one.

mathmate · Answer

Explain!

mathmate · Answer

Explain how you get those numbers in the equation, similar to how I did it in the first example.  Also, since this problem has more than one triangle involved, you have to mention which triangle you're working on.

mathmate · Answer

Are you back to question 6?

mathmate · Answer

You seem to have posted the same equation as #6.

mathmate · Answer

May I ask which triangle you're working on?

mathmate · Answer

The equation for #8 is definitely not the same as that of #6.
You're working with a triangle, so angles cannot add up to 360.

mathmate · Answer

|dw:1375438943785:dw|
Yes, it is confusing when we don't know which triangle we're working on.
Can you tell me which triangle you're working on, out of:
1. AOT
2. ABT
3. BOT