Construct a ∆ABC whose perimeter is 12 cm and whose base angle are 45° and 60°.

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Solution

Steps of construction:
1. Draw a line segment XY = 12 cm.
2. Construct an angle of 45 $°$ and bisect it to get $∠$ YXP.
3. Construct an angle of 60 $°$ and bisect it to get $∠$ XYQ.
4. The ray XP and YQ intersect at A.
5. Draw the right bisectors of AX and AY, cutting XY at B and C, respectively.
6. Join AB and AC.
Thus, $△$ ABC is the required triangle.

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