Answer :

We know that the sum of all angles of a triangle = 180°

∴ ∠A + ∠B + ∠C = 180°

⇒ ∠C + 45° + 105° = 180°

∴ ∠C = 180° - 150° = 30°

Construction Steps:

Step 1: Draw BC = 7 cm.

Step 2: At point B, draw a ray at ∠B = 45°.

Step 3: At C, draw a ray making an angle of 30° with BC intersecting the previous ray at A.

Step 4: Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.

Step 5: Locate 4 points B_{1}, B_{2}, B_{3} and B_{4} on BX so that BB_{1} = B_{1} B_{2} = B_{2} B_{3} = B_{3} B_{4}.

Step 6: Join B_{4}C and draw a line through B_{3} || B_{4}C to intersect BC at C′.

Step 7: Draw a line through C′ parallel to the line CA to intersect BA at A.

Thus, ΔA’BC’ is the required triangle.

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