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如題，唔該 16)In△PQR as shown ,S and T are the points on QR ad PR respectively. If ∠RPQ=53°，∠PQR=65° and TS⊥QR,find (a)∠PTS, (b)∠STP+∠TPQ+∠PQS+∠QST. 17) (a)Construct an obtuse- angled isosceles triangle (b)Is it possible to have teo obuse angles in a triangle?Why? 今晚之內要.... 要有過程，唔該曬

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16. In △PQR as shown, S and T are the points on QR ad PR respectively. If ∠RPQ ＝ 53°, ∠PQR ＝ 65° and TS⊥QR, find ( a ) ∠PTS, ( b ) ∠STP ＋ ∠TPQ ＋ ∠PQS ＋ ∠QST. Sol: ∠RPQ ＋ ∠PQR ＋ ∠QRP ＝ 180° 53° ＋ 65° ＋ ∠QRP ＝ 180° ∠QRP ＝ 62° ∠PTS ＝ ∠TSR ＋ ∠QRP ∠PTS ＝ 90° ＋ 62° ∠PTS ＝ 152° ( b ) ∠STP ＋ ∠TPQ ＋ ∠PQS ＋ ∠QST ＝ 152° ＋ 53° ＋ 65° ＋ 90° ＝ 360° Ans: ( a ) 152° ( b ) 360° 17 ( a ) Construct an obtuse-angled isosceles triangle ( b ) Is it possible to have two obtuse angles in a triangle? Why? Sol: ( a ) Draw a diagram yourself. Draw a △ABC AB ＝ AC, and ∠BAC ＞ 90° Then, it is an obtuse-angled isosceles triangle. ( b ) No. 三角形的內角和為 180°, 而鈍角大於 90°, 若一個三角形有兩個鈍角, 則內角和就會大於 180°. 所以, 一個三角形不可能有兩個鈍角. Send me a letter if any steps you don’t understand.

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