Four angles of a pentagon are equal and the fifth is 60°. Find the equal
angles and show that two sides of the pentagon Are parallel.
The sum of the n interior angles of an n-sided polygon is given by
(n-2)180°
A pentagon has 5 sides, so n = 5 and the sum of the interior angles is
(5-2)180° = (3)180° = 540°
The fifth angle is 60°, so the sum of the other 4 is 540°-60°=480°.
They are all equal, so each one is 480°/4 = 120° each
∠A, ∠B are supplementary because their measures are 60° and 120°
which have sum 180°
AE ∥ BC because consecutive interior angles A and B are supplementary, when
AE and BC are cut by transversal AB.
AB ∥ ED similarly.
Edwin
