A straight hedge runs parallel to a straight fence at the edge of a field. A footpath crosses both in a single straight line, and where the footpath crosses...
Question 1 Report
A straight hedge runs parallel to a straight fence at the edge of a field. A footpath crosses both in a single straight line, and where the footpath crosses the fence it makes an angle of 132 degrees with the fence.
- Work out the size of the angle the footpath makes with the hedge, on the same side as the marked angle. (3)
Answer Details
This question tests co-interior (allied) angles, which occur between two parallel lines cut by a transversal.
The hedge and fence are parallel, and the footpath is the transversal crossing both. The marked \(132^\circ\) angle where the footpath meets the fence, and the required angle where the footpath meets the hedge on the same side of the transversal, are co-interior angles, meaning they lie between the two parallel lines on the same side of the transversal. Co-interior angles between parallel lines always sum to \(180^\circ\):
\[132^\circ + \text{required angle} = 180^\circ\]So the required angle is:
\[180^\circ - 132^\circ = 48^\circ\][3] (identifying the co-interior angle relationship, stating the sum is \(180^\circ\), and subtracting to find \(48^\circ\))
Co-interior angles are the one pair of parallel-line angles that are supplementary (add to \(180^\circ\)) rather than equal; the other pairs, corresponding and alternate angles, are always equal. Checking whether the two marked angles are on the same side of the transversal, and between or outside the parallel lines, tells you which rule to apply.
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