Expert: Sherry Wallin - 4/18/2010

Question
Hi Sherry, I would be very grateful for some help please. I am stuck on an
equation and despite my best efforts am uncertain on how to tackle it. I would
be very grateful for some advice please. There is a picture of a quadrilateral shape (almost like a skewed diamond shape) with angle sizes at each point/corner. The question then reads: In this

quadrilateral, the sizes of the angles in degrees, are:
x+10 (at the top), 2x (left most side), 2x (at the bottom) and, 50 (right most side)
a) Use this information to write down an equation in terms of x

b) Work out the value of x

I attempted the equation by using brackets but lost myself in the process. I
started by thinking of the quadrilateral as totalling 360 degrees.
Therefore, I assumed
x = (x+10) + (2x) + (2x) + 50 divided by 360. I added up the numbers in brackets

and crossed out the x's to give me 10+2+2+50 = 64/360 = 18 but replacing 18 in
the x's for each angle does not total 360. Could you show me where I am going
wrong please. Thanks for your time
Regards
Gary

Answer
Gsry~
    You are right a quadrilateral has 4 sides and 4 interior angles. You are given a representation of x+10, 2x, 2x, and 50 so add them up and again you are right they should equal 180 degrees: x+10 + 2x + 2x + 50 = 180-> this is part a. When they say 'in terms of x' they mean where x is the variable.

5x + 60 = 180
5x + 60 - 60 = 180 - 60
5x = 300
5x/5 = 300/5
x = 60
So the angles measure 60+10, 2(60), 2(60), 50 -> 70deg, 120deg, 120deg, 70deg -> this is part b.

Math Prof