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Two vertices of a regular pentagon, in red, intersect with two vertices of a regular hexagon, in blue. What is the measure of the yellow angle?

 

 May 13, 2020

Best Answer 

 #1
avatar+21945 
+2

The formula for each interior angle of a regular polygon of n sides is:  (n - 2)(180o)/n

 

For a regular hexagon:  (6 - 2)(180o)/6  =  120o.

For a regular pentagon:  (5 - 2)(180o)/5  =  108o.

 

For the red triangle that is outside the blue hexagon, the two base angles are each: 

    (180o - 108o) / 2  =  36o.

This means that each base angle of the dark-red trapezoid is 108o - 36o  =  72o.

 

Subtracting this from the hexagon angle, we get  120o - 72o  =  48o

 May 13, 2020
 #1
avatar+21945 
+2
Best Answer

The formula for each interior angle of a regular polygon of n sides is:  (n - 2)(180o)/n

 

For a regular hexagon:  (6 - 2)(180o)/6  =  120o.

For a regular pentagon:  (5 - 2)(180o)/5  =  108o.

 

For the red triangle that is outside the blue hexagon, the two base angles are each: 

    (180o - 108o) / 2  =  36o.

This means that each base angle of the dark-red trapezoid is 108o - 36o  =  72o.

 

Subtracting this from the hexagon angle, we get  120o - 72o  =  48o

geno3141 May 13, 2020

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