A triangle and a Pentagon meet ...

Geometry Level 3

A B C D E ABCDE is a regular pentagon. F A D FAD is an equilateral triangle, such that points F F and E E are on the same side of line A D AD . What is the measure (in degrees) of ∠ F A B \angle FAB ?

Details and assumptions

Line A D AD bisects the plane into two half planes. 2 points will lie on the same side of line A D AD if they lie in the same half plane.


The answer is 132.

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Arron Kau by Arron Kau

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1 solution

We know that every angle of the pentagon measures 108 °. Also ADE is an isosceles triangle where their basal angles measures 36 °. ADF is a equilateral triangle. Therefore if we subtract 36 to 60 will give 24, then 108 plus 24 gives us the angle we ask that measures 132.

PD: Is recommended to draw all the data to better understand the problem.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Drawing a diagram is crucial to working on this problem.

Do you know how to show that every angle of the pentagon is 10 8 ∘ 108 ^\circ ?

yes

Vinayak Patil - 7 years, 10 months ago

In geometry problems solutions brilliant team should give the figure too. Because general people could not understand the figure due to that unable to give answer. Rest is OK. For my case I could not understand the problem by seeing the solution due to figure not available.

Abhay Rajput - 7 years, 10 months ago

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