Question

Construct a quadrilateral $ABCD$ in which $AB=3.6\text{cm},\angle ABC={80}^{\circ },BC=4\text{cm},\angle BAD={120}^{\circ }$, and $AD=5\text{cm}$.
Steps of construction are:
(i) Make $\angle BAY={120}^{\circ }$
(ii) Join $CD$
(iii) With $B$ as centre and radius equal to $4\text{cm}$, draw an arc, cutting $BX$ at $C$.
(iv) Draw $AB=3.6\text{cm}$
(v) With $A$ as centre and $5\text{cm}$ as radius, draw an arc, cutting $AY$ at $D$.
(vi) Make $\angle ABX={80}^{\circ }$
Choose the correct order of steps of construction.

• A. (i), (vi), (ii), (iv), (v), (iii)
• B. (i), (iii), (ii), (iv), (vi), (v)
• C. (i), (ii), (iii), (iv), (v), (vi)
• D. (iv), (vi), (iii), (i), (v), (ii)

Answer 1

The correct option is D (iv), (vi), (iii), (i), (v), (ii)

The correct steps of construction:
Step 1: Draw $AB=3.6\text{cm}$
Step 2: Make $\angle ABX={80}^{\circ }$
Step 3: With $B$ as centre and radius equal to $4\text{cm}$, draw an arc, cutting $BX$ at $C$.
Step 4: Make $\angle BAY={120}^{\circ }$
Step 5: With $A$ as centre and $5\text{cm}$ as radius, draw an arc, cutting $AY$ at $D$.
Step 6: Join $CD$