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Question

Construct a triangle whose perimeter is 10.4 cm and whose base angles are 45 and 120.
[3 Marks]

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Solution


[1 Mark]

Steps of construction:
1. Draw a line segment XY = 10.4 cm.
2. Make angle ∠LXY = ∠B = 45° and ∠MYX = ∠C = 120°.
3. Bisect ∠LXY and ∠MYX. Let these bisectors intersect at a point A (say).
4. Draw perpendicular bisectors PQ and RS of AX and AY, respectively.
5. Let PQ intersect XY at B and RS intersect XY at C.
6. Join AB and AC.

Then, △ ABC is the required triangle.
[2 Marks]

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