Question

Four angles if a pentagon are equal and the fifth is 60. Find the equal angles and show that the two sides of the pentagon are parrallel

Answer 1

Step-by-step explanation:

Sun of all interior angles of a polygon = (n-2)*180°

So for pentagon ie with 5 sides = (5-2)*180°

Which is equal to 3(180) = 540°

Given 4x + y = 540

y = 6p

4x + 60 = 540

4x = 480

x = 120°.

Theory : when a transversal intersects 2 lines, the 2 lines are parallel if and only if interior angles on the same side of the transversal are supplementary. (ie sum = 180°)

<A and <B are supplementary because <A+<B = 120 + 60 = 180°

<A+<E = 120 + 60 = 180

lines AB and EC are 2 lines cut by transversal AE.

So AB || EC.