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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 B1, B2, B3 and B4 on BX so that BB1 = B1 B2 = B2 B3 = B3 B4.

Step 6: Join B4C and draw a line through B3 || B4C 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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