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In a hexagon, three angles have the same measure. The measure of each of the congruent angles is twice the measure of the fourth angle and is half the measure of the fifth angle. The sixth angle measure 115°. What is the measure of the smallest angle?

Guest May 2, 2017
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The interior angles sum to 720°

 

So..let x be the measure of one of the congruent angles......and we have

 

3x   + (1/2)x   + 2x  + 115  =  720    simplify

 

5.5x + 115   = 720    subtract 115 from each side

 

5.5x  =  605        divide both sides by 5.5

 

x  = 110

 

The smallest angle =  (1/2)x  =  (1/2) * 110  =  55°

 

 

 

cool cool cool

CPhill  May 3, 2017

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