✔ 最佳答案
Question:
Refer to the figure. Find a + b + c + d - e.
https://s.yimg.com/tr/i/197117cd950d48bc9d1bab83cdbd86fe_A.png
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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/bb9f959e628248b8a5d57f24aebcdbf2_A.png
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/0ae39861088c47f198e93eab6ceed3a0_A.png
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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