Question

if line PQ and RS interest at point t, such the <PRT =40°,<RPT =95°and <TSQ =75,find <SQT.​

Answer 1

Step-by-step explanation:

∠PRT+∠RPT+∠PTR=180

∘

⇒90

∘

+45

∘

+∠PTR=180

∘

⇒135

∘

+∠PTR=180

∘

⇒∠PTR=180

∘

−135

∘

⇒∠PTR=45

∘

.

Also,

∠STQ=∠PTR

∠STQ=45

∘

(vertically opposite angles)

In ΔSQT

By angle sum property of triangle

∠SQT+∠STQ+∠TSQ=180

∘

∠SQT+75

∘

+45

∘

=180

∘

∠SQT+120

∘

=180

∘

∠SQT=180

∘

−120

∘

∠SQT=60

∘