Question

Is it possible to construct a unique quadrilateral ABCD with AB = 4cm, AD = 6 cm, $\angle ABC={60}^{\circ }$, $\angle DAB={75}^{\circ }$, and $\angle ADC={85}^{\circ }$? If yes, find the value of $\angle BCD$.
(4 marks)

Answer 1

We have 5 measurements. Thus, a quadrilateral can be constructed.

Step 1: Draw AB = 4 cm.

Step 2: Draw $\angle DAB={75}^{\circ }$ and mark AD = 6 cm on it.

Step 3: At D, draw $\angle ADC={85}^{\circ }$ and extend the line along $\angle ADC$.

Step 4: Draw $\angle ABC={60}^{\circ }$ and extend the line along $\angle ABC$ such that it intersects the line extending along $\angle ADC$. Mark the point of intersection as C.

Step 5: Join the points A,B,C and D. Measure $\angle BCD$. It is equal to ${140}^{\circ }$_.

(2.5 marks)

Alternatively :

$\angle BCD$ $={360}^{\circ }-(\angle ABC+\angle DAB+\angle ADC)$
= ${360}^{\circ }-({60}^{\circ }+{75}^{\circ }+{85}^{\circ })$
= $({360}^{\circ }-{220}^{\circ })={140}^{\circ }$

(1.5 marks)