GCSE Mathematics (9-1)
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    16.5 Geometrical reasoning and proof — Practise with help

    Try each question before opening a hint. Open the next part only when you need it.

    Warm-up: remember

    1. Find a triangle angle when the other two are 48∘48^\circ and 67∘67^\circ.
    2. Find the interior sum of a pentagon.
    Check your answers
    1. 65∘65^\circ. 2. 540∘540^\circ.

    Practise with help

    1. Parallel lines give one angle of 64∘64^\circ. Find and justify the co-interior angle.

    Hint

    Co-interior angles on parallel lines total 180∘180^\circ.

    One step

    Let the co-interior angle be xx.

    Full working x+64=180co-interior angles total 180∘x+64=180 \qquad \text{co-interior angles total }180^\circ x=180−64=116∘x=180-64=116^\circ

    The angle is 116∘116^\circ.

    2. A triangle has angles 52∘52^\circ, x∘x^\circ and (x+20)∘(x+20)^\circ. Find xx and give a reason.

    Hint

    Mark the known angles and identify their relationship before calculating.

    One step

    The interior angles of a triangle total 180∘180^\circ. Use this fact to form an equation.

    Full working 52+x+(x+20)=180triangle angles total 180∘52+x+(x+20)=180 \qquad \text{triangle angles total }180^\circ 2x+72=1802x+72=180 2x=1082x=108 x=54∘x=54^\circ

    3. Earlier learning. Work out: 7+5×37+5\times3. Explain which operation you do first.

    Hint

    Use the order of operations.

    One step

    Calculate 5×35\times3 before adding.

    Full working

    7+5×3=7+15=227+5\times3=7+15=22. Multiplication comes before addition.

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