20.
(i) From the figure, find the value of p, q, r if
(a) pº = q° = rº
(b) pº = 2rº and q = 3rº
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MATHS
From the adjacent figure find the value of (i) ∠PRS (ii) ∠PTS (iii) ∠STR (iv) ∠PRQ
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December 20, 2019
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Prajapati Kotturi
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ANSWER
From △PQR,∠RPQ+∠PQR+∠PRQ=180
∘
using angle sum property
⇒50
∘
+35
∘
+∠PRQ=180
∘
⇒∠PRQ=180
∘
−85
∘
=95
∘
AS QS is a straight line ∠QRS=180
∘
⇒∠QRS=∠QRT+∠TRS
⇒180
∘
=95
∘
+∠TRS
⇒∠TRS=180
∘
−95
∘
=85
∘
In △TRS,∠TRS+∠RST+∠STR=180
∘
⇒85
∘
+45
∘
+∠STR=180
∘
⇒∠STR=180
∘
−130
∘
=50
∘
Again PR is a straight line and R is a point on the line PR
⇒∠PTR=180
∘
⇒∠PTS+∠STR=∠PTR
⇒∠PTS+50
∘
=180
∘
∴∠PTS=180
∘
−50
∘
=130
∘
Hence (i)∠PRS=∠TRS=85
∘
(ii)∠PTS=130
∘
(iii)∠STR=50
∘
and (iv)∠PRQ=95
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