Question

The diagram shows a regular pentagon with two of its diagonals.If all the diagonals are drawn ,into how many areas will the pentagon be divided?​​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Total angle sum for pentagon = 3*180 = 540 degrees. So each vertex angle = 540/5 = 108 degrees.

Isosceles Triangles <-> Angles

Two sides and a vertex form an obtuse isosceles triangle, two such are shaded here.

Since obtuse vertex angle EAB = 108 and two equal base angles have sum = 180 – 108 = 72, acute base angles such as CAB = 36 degrees.

Also, angle CAD = angle EAB - 2*36 = 36 degrees, so the 2 diagonals from a vertex such as A trisect the vertex angle; that is, they divide the vertex angle into 3 equal 36-degree angles.

Finally, triangle DAC is isosceles since each of the base angles ACD and ADC are equal to 108 – 36 = 72 degrees.