A destination board hung above the platform at a busy bus interchange is a quadrilateral metal frame. Its four interior angles, in degrees, are \(2x\), \(3x...
Question 1 Report
A destination board hung above the platform at a busy bus interchange is a quadrilateral metal frame. Its four interior angles, in degrees, are \(2x\), \(3x\), \(x + 40\) and \(4x - 10\), as shown.
- Form an equation in \(x\) using the angle sum of the frame, and simplify it. (2)
- Solve your equation to find the value of \(x\). (2)
Answer Details
Every quadrilateral has interior angles summing to \(360^\circ\), since it can be split into two triangles, each contributing \(180^\circ\). Writing this fact as an equation lets the four angle expressions be combined and solved for \(x\).
- \(2x + 3x + (x + 40) + (4x - 10) = 360\)
Collecting the \(x\) terms and the numbers separately: \(10x + 30 = 360\). [2 marks] - \(10x = 330\)
\(x = 33\). [2 marks]
As a check, substitute \(x = 33\) back into each angle: \(2(33)=66^\circ\), \(3(33)=99^\circ\), \(33+40=73^\circ\), \(4(33)-10=122^\circ\); these total \(66+99+73+122=360^\circ\), confirming the solution. Combining like terms before solving, rather than solving with all four terms separately, is what keeps this kind of equation manageable.
Download The App On Google Playstore
Everything you need to excel in your exams
