Theory question 102
Linear and Simultaneous Equations(a) Solve the equation: ⅔(3x − 5) − ⅗(2x − 3) = 3
(b) In the diagram, ∠STQ = m, ∠TUQ = 80°, ∠UPQ = r, ∠PQU = n and ∠RQT = 88°. Find the value of (m + n).
Show the model answer
Model answer
(a) Multiply by 15: 10(3x − 5) − 9(2x − 3) = 45 → 12x − 23 = 45 → x = 68/12 = 5⅔
(b) ∠UQT = 180° − n − 88° = 92° − n (angles on straight line PQR)
∠UTQ = 180° − m (angles on straight line PUTS)
In triangle UQT: 80° + (92° − n) + (180° − m) = 180° → m + n = 172°
Explanation
Express the angles of triangle UQT in terms of m and n.