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¨§¾ÔÊÙ¨¹ìÇèÒ x = 30°
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ãËé BP = L
(1) ∠APC = 120° áÅÐ ∠BPC = 140° ⇒ ∠APB = 100°
(2) ¡Ó˹´¨Ø´ Q à»ç¹ÀÒ¾Êзé͹¢Í§¨Ø´ P ¼èÒ¹ BC ⇒ ∆BCQ ≅ ∆BCP ⇒ BQ = BP , CQ = CP, ∠CBQ = ∠CBP = 30° áÅÐ ∠BCQ = ∠BCP = 10°
∵ BP = BQ áÅÐ ∠PBQ = 60° ⇒ ∆BPQ à»ç¹ ∆´éÒ¹à·èÒ ⇒ PQ = BP ⇔ PQ = L
(3) ¡Ó˹´¨Ø´ R º¹ AC ·Õè·ÓãËé CR = CP ⇔ CR = CQ
¨ÐàËç¹ÇèÒ ∆CPR ≅ ∆CPQ ´éǤÇÒÁÊÑÁ¾Ñ¹¸ìẺ ´-Á-´ (CP = CP, ∠PCR = ∠PCQ, CR = CQ) ⇒ PR = PQ ⇔ PR = L
∵ CP = CR ⇔ ∆CPR à»ç¹ ∆˹éÒ¨ÑèÇ ·ÕèÁÕ ∠C (= 20°) à»ç¹ÁØÁÂÍ´ ⇔ ∠CPR = 80° áÅÐ ∠CRP = 80° ⇔ ∠APR = 40° áÅÐ ∠ARP = 100°
∵ ∠PAR = ∠APR ⇔ ∆APR à»ç¹ ∆˹éÒ¨ÑèÇ ·ÕèÁÕ ∠R à»ç¹ÁØÁÂÍ´ ⇔ AR = PR ⇔ AR = L
(4) ¡Ó˹´¨Ø´ S à˹×Í PR ·Õè·ÓãËé PS = RS = PR (= L) ⇔ ∆PRS à»ç¹ ∆´éÒ¹à·èÒ ⇒ ∠RPS = ∠PRS = 60°
∵ AR = RS ⇔ ∆ARS à»ç¹ ∆˹éÒ¨ÑèÇ ·ÕèÁÕ ∠R (= 160°) à»ç¹ÁØÁÂÍ´ ⇔ ∠RAS (= ∠ASR) = 10° ⇔ ∠PAS = 30°
(5) ÊѧࡵÇèÒ ∆ABP ≅ ∆APS ´éǤÇÒÁÊÑÁ¾Ñ¹¸ìẺ ´-Á-´ (AP = AP, ∠APB = ∠APS, BP = PS) ⇒ ∠BAP = ∠PAS ⇔ x = 30° Q.E.D.
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