Angles of a decagon

[neno89]

Seven of the angles of a decagon have measures whose sum is 1220 of the remaining 3 angles, exactly 2 are complementary and exactly 2 are supplementary. Find the measures of these 3 angles. Can someone help me. Thank you.

 

[galactus]

The angle sum of a polygon is 180(n-2). So, the angle sum of your decagon is

180(10-2)=180*8=1440. See?.

7 of the angles total 1220 degrees. So, the remaining three must have angle total of 1440-1220=220 degrees.

Complementary means they sum to 90; supplementary means they sum to 180.

You could call the angles x, y, and z. The total sum is 220. Remember, there are 3 angles, 2 are supplementary and 2 are complementary. That means one is shared.

You can set up a simple system of 3 equations with 3 variables and solve.

 

[neno89]

You can set up a simple system of 3 equations with 3 variables and solve

.[/quote]

I don't understand how to set up the 3 equations.

 

[stapel]

Take the variable names the tutor gave you, and plug them into the relationships the tutor gave you. Please reply with what you've tried. Thank you.

Eliz.

 

[neno89]

so it would be x+y+z = 220? but that doesn't get me anywhere. and what would be the other 2 equations? x+y = 90 and x+z = 180? I'm getting confused at that part.

 

[Mrspi]

so it would be x+y+z = 220? but that doesn't get me anywhere. and what would be the other 2 equations? x+y = 90 and x+z = 180? I'm getting confused at that part.

I think the three equations you've written:
1) x+ y + z = 220
2) x + y = 90
3) x + z = 180

will get you the correct answer!

Subtract 2) from 1):
x + y + z = 220
-x - yxxx = -90
---------------
xxxxxx z = 130

Now, can you take it from here?