20 In the diagram what is the sum of the measure of angles 1

20. In the diagram, what is the sum of the measure of angles 1, 2, 3, 4, and 5? Angle Summa.

Solution

For a 5-sided polygon (pentagon) this is (5-2)*180° = 3*180°=540°
Since all 5 angles of a regular pentagon are equal, each
interior angle of the regular pentagon is 540/5 = 108°
Its suppplement is found by subtracting 180°-108°=72°
That 72° angle is one of the base angles of an isosceles

triangle. So we\'ll mark the other base angle 72° also
Now we can find the angle at the top point of the star by
adding the two equal base angles and subtracting from 180°.

72° + 72° = 144°
180° - 144° = 36°

So each point of the star is 36°

In a regular pentagram (five pointed star) each point is 36^o so the sum of all angle is 180^o.

So, the angle(1+2+3+4+5) = 5 x 36 = 180^o

16. In the given figure the angles are not defined in which position they are

this could be solved by sector formula