polygons!

Geometry Level 1

find the value of angles C and E, if pentagon ABCDE is a regular polygon.

this problem appeared in the annual national assessment,term 2,in south africa 2014

c=108,e=90 c=46,e=109 c=36,e=108 c=108,e=36

Vilashni Mottian by vilashni mottian , 21, South Africa

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

11 solutions

Robert Brown
Dec 20, 2014

Very simple solution with the answers given. E is not 90 nor is it more than 90. The only solution with E being less than 90 showed it as 36. Therefore, the only answer that could be correct is c=108, e=36.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

why E not more than 90 ?

Anil Ram - 6 years, 5 months ago
Francis Reppert
Dec 21, 2014

Since Pentagon ABCDE is a regular polygon, Angle C is 108. Triangle ABE is an isosceles triangle. Angle A is the vertex angle, which we know is 108. Then, the Base Angle Theorem gives the angles B & E are the same. So 180 - 108 = 72, then 72/2 = 36.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

C=(n-2)180/n =3×180/5 108

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Jessica Cas
Dec 27, 2014

180(n-2) = 180(5-2) = 540. 540/n = 540/5 = 108. each angles has 108 degrees. C=108. A=108. A triangle has 180 degrees of angles. Since B=E, 180=A+B+E. 180=A+E+E or 180=A+2E. 180=108+2E. 72=2E. E=36.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Anna Anant
Dec 27, 2014

Sum of 5 interior angles of pentagon is 540, where each angle is 108.... this gives c=108... in triangle abe ab=ae and 108+b+e=180 where b=e... gives e=36

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Erielle Senique
Dec 27, 2014

given that 180(5-2)= total no. of interior angles of a regular pentagon so 180(3)=540 then 540/5= degree of each interior angle so 540/5=108. So C=108 then also A=108 then 180-108=72 because the total interior angles of a triangle is 180 so angle B + angle E= 72 and because the triangle is isosceles, so angle B = angle E so 72/2=36 so angle B and angle E = 36

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Chandresh Shah
Dec 27, 2014

Sum of internal angles of a regular Pentagon is. 540 so angles c is 540/5 = 108 Triangle ABE is equvilateral with Angle A is 108, so B + E is 180-108 = 72 degrees therefore angle B is 72/2=36

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Tracing the diagonal of the pentagon, we obtain three triangles. The sum of the interior angles of the pentagon then coincides with the sum of the interior angles of the three triangles, ie 3 times 180º. So every angle of the pentagon measures (3 X 180º) divided by 5 = 108º. As C = A, and the triangle ABE is isosceles, then E = (180º - 108º) divided by 2 = 36º.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Maliha Amanat
Dec 22, 2014

As shown, C is obtuse angle i.e greater than 90 where as E is acute less than 90. So, from the options C must be greater and E must be less than 90 respectively., but E must not be 90 degrees... So. Simple!

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Maniraj Kunkatla
Dec 20, 2014

Sum of internal angles of a regular Pentagon is. 540 so angles c is 540/5 = 108 Triangle ABE is equvilateral with Angle A is 108, so B + E is 180-108 = 72 degrees therefore angle B is 72/2=36

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Bk Lim
Dec 13, 2014

c=180-(360/5)=108 e=(180-c)/2 = 36

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...