Question 969745: Two angles of a quadrilateral measure 167° and 108°. The other two angles are in a ratio of 7:10. What are the measures of those two angles?
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 35 and 50 degrees ANSWER
The interior angles of a quadrilateral measure to 360 degrees
Two of them are known and are 167 and 108. They add to 275 degrees.
The other two angles must sum to (360-275)=85 degrees.
They are in a ratio of 7:10
The sum of these two numbers is 17, and (85/17)=5
So 5 * (7:10) will be 35:50, keeping the same ratio balance.
The other two angles are 35 and 50 degrees respectively.
The sum of all 4 angles is 360 degrees.
Note, with a 7:10 ratio, you could also just start with 7 and 10 degrees, then 14 and 20 degrees then 21 and 30 degrees until you reached 35 and 50 degrees. If you can recognize that the sum of the numbers in the ratio is a factor of the number of degrees you need, then the (85/17) is faster. Simply doubling, tripling, etc. of the ratio will get you to the answer, too.
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Two angles of a quadrilateral measure 167° and 108°. The other two angles are in a ratio of 7:10. What are the measures of those two angles?
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Sum of all the angle is 2*180 = 360
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sum of the unknown angle is 360-(167+108) = 360-275 = 85 degrees
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Equation:
7:10 is the same as 7x:10x
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7x+10x = 85
17x = 85
x = 5
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Ans:
smaller angle:: 7*5 = 35 degrees
larger angle:: 10*5 = 50 degrees
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Cheers,
Stan H.
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