Question

Construct a rhombus ABCD in which ∠A =75° and AB = 4 cm.

Answer 1

Given:

AB = 4 cm, ∠A = 75°.

ABCD is a rhombus all sides equal; adjacent angles are supplementary.

Step-wise calculation (construction with ruler and compass):

1. Draw segment AB = 4 cm.
2. At A, construct ray AD so that ∠DAB = 75°. On this ray mark point D so that AD = 4 cm.
3. At B, construct ray BC so that ∠ABC = 180° – 75° = 105°. On this ray mark point C so that BC = 4 cm. We use 105° at B because in a rhombus adjacent angles sum to 180°.
4. Join C to D to complete the quadrilateral ABCD.
5. Check: AB = BC = CD = DA = 4 cm by construction and ∠A = 75°, so ABCD is the required rhombus.

ABCD constructed as above is a rhombus with ∠A = 75° and side length 4 cm.