Two diagonal lines are painted across a car park to mark a pedestrian crossing point, as shown. The two marked angles are vertically opposite each other, wi...
Question 1 Report
Two diagonal lines are painted across a car park to mark a pedestrian crossing point, as shown. The two marked angles are vertically opposite each other, with sizes \((6x-10)^{\circ}\) and \((4x+30)^{\circ}\).
Work out the value of \(x\). (2)
Answer Details
Vertically opposite angles, formed where two straight lines cross, are always equal; this fact turns the two expressions for the marked angles directly into an equation in \(x\).
Setting the two vertically opposite angles equal: \(6x-10=4x+30\). [1 mark]
Subtracting \(4x\) from both sides and adding \(10\) to both sides: \(2x=40\), so \(x=20\). [1 mark]
Checking both expressions with \(x=20\): \(6(20)-10=110\) and \(4(20)+30=110\), which agree, confirming the vertically opposite angles are indeed equal.
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