Answer:
Part 1)
Part 2)
Part 3)
Part 4)
Part 5) , or
Part 6) , or
Step-by-step explanation:
see the attached figure to better understand the problem
In this problem we have an isosceles trapezoid
Part 1) Find the measure of angle P
Find the value of side PD
we have that
---> by addition segment postulate
----> by isosceles trapezoid
so
substitute the given values
In the right triangle PSD
substitute the given values
Part 2) Find the measure of angle PST
we know that
In a trapezoid ST ║ RP
so
---> by consecutive interior angles
we have
substitute
Part 3) Find the measure of angle T
we know that
In this problem we have an isosceles trapezoid
so
we have
therefore
Part 4) Find the measure of angle R
we know that
In this problem we have an isosceles trapezoid
so
we have
therefore
Part 5) Find the measure of segment PS
we know that
In the right triangle PSD
Applying the Pythagorean Theorem
substitute the given values
Part 6) Find the measure of segment TR
we know that
TR=PS ---> by isosceles trapezoid
we have
therefore