Given: st ║ rp , sd ⊥ pr , sp = tr, sd = 5, st = 15, pr = 24 find: m∠p, m∠pst, m∠t, m∠r, ps, tr

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

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