JAMB Mathematics 2023 Paper

∠PQR + ∠PSR = 180o (opp. angles of cyclic quad. are supplementary)

⇒ 5$x$ - $y$ + 10 + (-2$x$ + 3$y$ + 145) = 180⇒ 5$x$ - $y$ + 10 - 2$x$ + 3$y$ + 145 = 180⇒ 3$x$ + 2$y$ + 155 = 180⇒ 3$x$ + 2$y$ = 180 - 155⇒ 3$x$ + 2$y$ = 25 ----- (i)∠QPS + ∠QRS = 180o (opp. angles of cyclic quad. are supplementary)⇒ -4$x$ - 7$y$ + 150 + (2$x$ + 8$y$ + 105) = 180⇒ -4$x$ - 7$y$ + 75 + 2$x$ + 8$y$ + 180 = 180⇒ -2$x$ + $y$ + 255 = 180⇒ -2$x$ + y = 180 - 255⇒ -2$x$ + $y$ = -75 ------- (ii)⇒ $y$ = -75 + 2$x$ -------- (iii)Substitute (-75 + 2$x$) for $y$ in equation (i)

⇒ 3$x$ + 2(-75 + 2$x$) = 25

⇒ 3$x$ - 150 + 4$x$ = 25⇒ 7$x$ = 25 + 150⇒ 7$x$ = 175

⇒ $x = \frac{175}{7} = 25$

From equation (iii)

⇒ $y$ = -75 + 2(25) = -75 + 50⇒ $y$ = -25∴ $x$ + $y$ = 25 + (-25) = 0