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Question 1042170: Two angles of a quadrilateral measure 20 degrees and 170 degree. The other two angles are in a ratio of 2:15. What are the measures of those two angles?
(The ratio factor is what has not yet been taught as I am entering 7th grade, but this is a problem given and have had no luck finding a resource to explain it... any help is appreciated...thanks, Caleb)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
We have four angles. Let's call them A,B,C,D.
The angles
A = 20
B = 170
are given to us
The other angles (C and D) are unknown.
We may not know the values, but we know how they're connected.
They are in a ratio of 2:15, so that means
C = 2*k
D = 15*k
where k is some positive real number.
With ANY quadrilateral, the four angles always add to 360 degrees. So
A+B+C+D = 360
Plug in the given values/expressions to get
20+170+2k+15k = 360
Let's solve for k.
20+170+2k+15k = 360
190+17k = 360
17k+190 = 360
17k+190-190 = 360-190 ... Subtract 190 from both sides
17k+0 = 170
17k = 170
17k/17 = 170/17 ... Divide both sides by 17
k = 10
Since k = 10, we can use this to finally determine what C and D are
C = 2*k = 2*10 = 20 degrees
D = 15*k = 15*10 = 150 degrees
So we have these four angles
A = 20 degrees
B = 170 degrees
C = 20 degrees
D = 150 degrees
Notice how
A+B+C+D = 20+170+20+150 = 360 degrees
So that confirms the answer
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