A destination board fixed above a busy train platform is cut from a single sheet of dark metal into a quadrilateral tile, so that passengers can read it fro...
Question 1 Report
A destination board fixed above a busy train platform is cut from a single sheet of dark metal into a quadrilateral tile, so that passengers can read it from far away. Three of its interior angles measure \(95^\circ\), \(88^\circ\) and \(102^\circ\), and the fourth is marked \(x\), as shown.
Work out the value of \(x\). (3)
Answer Details
This question tests the angle sum of a quadrilateral, which follows from splitting it into two triangles, each contributing \(180^\circ\).
The interior angles of any quadrilateral sum to \(360^\circ\). [1 mark]
Adding the three known angles gives \(95 + 88 + 102 = 285^\circ\). [1 mark]
The fourth angle is the remainder: \(x = 360 - 285 = 75^\circ\). [1 mark]
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