(a) Solving the eqns of the two lines simultaneously: x + 2y = 7 - - -- - - - - - -(i) x - y = 4 - - - - - - - - - - - -(ii) subtract eqn (ii) from (i) x - x + 2y - (- y) = 7 - 4 3y = 3 y = 1 put y = 1 into eqn (ii) x - 1 = 4 x = 4 + 1 = 5 The point of intersection of lines is (5, 1) ⇒ If the line passes through Origin (0, 0) and (5, 1) Using: \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{y - y_1}{x - x_1}\) \(\frac{1 - 0}{5 - 0} = \frac{y - 0}{x - 0}\) \(\frac{1}{5} = \frac{\text{y}}{\text{x}}\) Therefore, the equation of the line = x - 5y = 0 (b) Given that the ratio of the interior angle to the exterior angle of a regular polygon = 4: 1 Thus, I = 4E But, the sum of the interior angles and the exterior angles of a regular polygon = 180 i.e. I + E = 180 4E + E = 180 5E = 180 E = \(\frac{180}{5}\) = 36º Since, I = 4E = 4 x 36 = 144º (ii) value of the exterior angle = 36º (i) Number of sides of the polygon = \(\frac{360}{\text{n}}\) = E, n = \(\frac{360}{36}\) = 10 (since E = 36º) (iii) Sum of the interior angles of the polygon. = (n - 2)180 = (10 - 2)180 = 8 x 180 = 1,440.