Q1) The parallel sides (DC and AB ) of trapezium are 60cm and 77cm respectively The other two sides - Maths - Triangles

Question

Q1) The parallel sides (DC and AB ) of trapezium are 60cm and
77cm respectively The other two sides (AD and BC ) are 25cm and
26cm respectively Find the area of the trapezium ABCD
Q2) In a triangle, PT is perpendicular to QR and PS bisects
angle QPR If angleQ=65 and angleR=33, find angleTPS

Priyanka Kedia · Accepted Answer

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$I n t r i a n g l e P Q R, PS i s t h e b i \sec t o r o f ∠ Q P R, s o, ∠ R P S = ∠ P Q S = x S i n c e s u m o f a n g l e s o f a t r i a n g l e = 180^{0} T h e r e f o r e, ∠ P + ∠ Q + ∠ R = 180^{0} \Rightarrow (∠ Q P S + ∠ R P S) + ∠ Q + ∠ R = 180^{0} \Rightarrow (x + x) + ∠ Q + ∠ R = 180^{0} \Rightarrow x = 90^{0} - (\frac{∠ Q + ∠ R}{2}) \Rightarrow x = 90^{0} - (\frac{65^{0} + 33^{0}}{2}) \Rightarrow x = 41^{0} N o w, i n r i g h t t r i a n g l e C A N, ∠ R P T + ∠ R = 90^{0} \Rightarrow (x + ∠ S P T) + 33^{0} = 90^{0} \Rightarrow ∠ S P T = 90^{0} - 33^{0} - 41^{0} \Rightarrow ∠ S P T = 16^{0}$

Q1) The parallel sides (DC and AB ) of trapezium are 60cm and 77cm respectively. The other two sides (AD and BC ) are 25cm and 26cm respectively . Find the area of the trapezium ABCD. Q2) In a triangle, PT is perpendicular to QR and PS bisects angle QPR . If angleQ=65 and angleR=33, find angleTPS.

Q1) The parallel sides (DC and AB ) of trapezium are 60cm and 77cm respectively. The other two sides (AD and BC ) are 25cm and 26cm respectively . Find the area of the trapezium ABCD.

Q2) In a triangle, PT is perpendicular to QR and PS bisects angle QPR . If angleQ=65 and angleR=33, find angleTPS.