? 發問時間： 科學及數學數學 · 2 個月前

# Maths problem: how to do, thanks?

### 1 個解答

• 匿名使用者
2 個月前
最佳解答

Question：

Refer to the figure. Find a + b + c + d - e.

https://s.yimg.com/tr/i/197117cd950d48bc9d1bab83cd...

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Solution：

Method 1

a + b + c + d + reflex ∠PTS = (5 - 2)×180° ...... ( ∠ sum of polygon [simple concave] )

a + b + c + d + (360° - e) = 540° ...... ( ∠s at a pt. )

a + b + c + d - e = 540° - 360° = 180°

Method 2

Joint PS.

https://s.yimg.com/tr/i/bb9f959e628248b8a5d57f24ae...

a + b + c + d + ∠TPS + ∠TSP = (4 - 2)×180° ...... ( ∠ sum of polygon [convex] )

a + b + c + d + (180° - e) = 360° ...... ( ∠ sum of Δ )

a + b + c + d - e = 360° - 180° = 180°

Method 3

Joint QT and QS. Also, extend QT to U.

https://s.yimg.com/tr/i/0ae39861088c47f198e93eab6c...

a + b + c + d - e

= a + (∠PQT + ∠SQT + ∠RQS) + c + (∠RSQ + ∠QST) - e

= [(a + ∠PQT) + (∠SQT + QST)] + (∠RQS + c + ∠RSQ) - e

= (e) + (180°) - e ...... ( ext. ∠ of Δ and ∠ sum of Δ )

= 180°

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