Question

in the following figure, QT PR, TQR-40 and SPR=30, Find TRS and PSQ
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Answer 1

in triangle trs

qtr+tqr+qrt =180. (angle sum property)

40+90+TRQ=180

TRQ=180-130

=50

TRS can also be written as TRQ

SO.,TRS=50°

now angle PSQ=SPR+PRS

(sum of both opposite angle is equal to exterior angle)

PSQ=50+30

PSQ=80°

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Answer 2

In ∆TQR, we get :

m∠TQR + m∠TRQ +m∠QTR = 180°

Therefore, 40° + m∠TRQ + 90° = 180°

or, m∠TRQ = 50°

Therefore, m∠TRS = 50° also because ∠TRQ and ∠TRS both have same vertex R at a fixed point.

Now, m∠PSQ = m∠SPR + m∠PRS

or, m∠PSQ = 30° + 50°

or, m∠PSQ = 80°

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