Question

solve these questions

Answer 1

To prove:

∠P +∠Q+ ∠ R+∠S+∠T = 2(right angle) = 180°.


Proof:

In ΔBTR,

∠T+∠R + ∠BTR =180° (angle sum property of Δ) ------- (i)


In ΔAQS

∠Q+∠S + ∠QAS =180°(angle sum property of Δ) ---(ii)


In ΔPER

∠P+∠R +∠PER = 180°(angle sum property of Δ) ---(iii)


In ΔTQD
∠T +∠Q +∠TQD =180°(angle sum property of Δ) ----(iv)


In ΔPSC
∠P +∠S +∠PSC = 180°(angle sum property of Δ) ----(v)



Adding all 5 equations,

2(∠P +∠Q+ ∠ R+∠S+∠T ) + ∠BTR+∠QAS+∠PER+∠TQD+∠PSC= 5(180°) = 900°

You might be familiar that the sum of all interior angles on Pentagon equals 180°.

(If not try searching a 7th or 8th standard maths text books)

2(∠P +∠Q+ ∠ R+∠S+∠T ) + 540° = 900°

2(∠P +∠Q+ ∠ R+∠S+∠T ) = 900°- 540° = 360°

∠P +∠Q+ ∠ R+∠S+∠T = 360°/2 = 180°.


Hence proved.