Question

in a regular pentagon abcde , calculate the number of degrees in the angle abc and prove that bc || ad​

Answer 1

Answer:

If in a regular pentagon ABCDE, how do you calculate the number of degrees in the angle ABC and how do you prove that BC||AD?

Girija Warrier

Answered 7 months ago

Degree measure of any interior angle of a regular polygon = {(n-2)*180} / n , where n is the number of sides

So, <ABC of regular pentagon =

{(5–2)*180} / 5 = 540 / 5 = 108 deg

TO PROVE: BC // AD

CONSTRUCTION: Join A & D

PROOF: In tri EAD, ED = EA ( sides of regular polygon)

=> <EAD = EDA ( isosceles triangle)

=> <CDA = <BAD = y ( since <A = <D )

Now, in quadrilateral ABCD

The sum of all 4 angles = 360 deg

=> 2y + 2*108 = 360

=> 2y = 360- 216 = 144

=> y = 72 deg

Now, since <CBA + <DAB = 108+72 =180 deg

=> BC // AD ( as consecutive interior angles are supplementary)