Answer :

To construct a ΔABC, we first need to findC

We know that,

Sum of angles of a triangle = 180°

⇒ ∠A +B +C = 180°

105° + 45° +C = 180°

150° +C = 180°

⇒ ∠C = 30°

Now, we construct ΔABC

Steps of construction:

1. Draw base BC = 7cm

2. With the help of compass, draw an angleB = 45°

3. With the help of compass, drawC = 30°

4. Mark point A where two rays intersect

ΔABC is the required triangle

Now, we need to make a triangle which is times its size

Steps of construction:

1. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A

2. Mark 4 (the greater of 3 and 4 in ) points B1, B2, B3, B4 on BX so that BB1 = B1B2 = B2B3 = B3B4

3. Join B4C and draw a line through B3 (the 3rd point, 3 being smaller of 3 and 4 in ) parallel to B4C, to intersect BC at C’

4. Draw a line through C’ parallel to the line AC to intersect AB at A’

Thus, A’BC’ is the required triangle.

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