The measure of ∠S, ∠K, ∠E, and ∠P is 60°, 120°, 120°, and 60°, respectively. While the perimeter of EPSK is 40 units.
What is a Trapezoid?
A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
Given KE=OS=8, but OS is the radius of the circle, therefore, it can be written as,
OS = OP = KE = OK = OE = radius of the circle = 8 units.
Since in ΔOEK all sides are equal it is an equilateral triangle therefore, the measure of the angle ∠EOK is 60°.
As the measure of the angle, ∠EOK is 60°, the measure of the angle, ∠KOS and ∠EOP will be 60° each.
Also, in ΔSOK and ΔPOE, the sides OS = OP = KE = OK = OE are equal, they are equilateral triangles as well.
Therefore, the measure of ∠KSO and ∠EPO will be 60° each.
The angles at the end of the non-parallel sides of a trapezium are supplementary. Therefore, we can write,
∠KSO + ∠SKE= 180°
∠SKE = 120°
Similarly, the measure of the ∠PEK is 120°.
Further, it is known that the measure of the sides OS=OP=PE=EK=KS = 8 units, therefore, the perimeter of the trapezium is,
Perimeter = OS + OP + PE + EK + KS = 8+8+8+8+8 = 40 units.
Hence, the measure of ∠S, ∠K, ∠E, and ∠P is 60°, 120°, 120°, and 60°, respectively. While the perimeter of EPSK is 40 units.
Learn more about Trapezoid:
https://brainly.com/question/8643562
#SPJ2
