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# help

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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

#1
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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
+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

geno3141 May 13, 2020