a) Show that $\angle D O A=105^{\circ}$
b) Show that the length of DA is $127 \mathrm{~m}$ (to the nearest metre)
c) Hence, find the perimeter and area of the entire block of land $A B C D$

Answer

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Answer

$\angle DOA = 360^\circ - \angle AOD - \angle DAO = 360^\circ - 120^\circ - 135^\circ = 105^\circ$

Steps

Step 1 ：$\angle AOC = 180^\circ - \angle BOC = 180^\circ - 120^\circ = 60^\circ$

Step 2 ：$\angle AOD = 180^\circ - \angle AOC = 180^\circ - 60^\circ = 120^\circ$

Step 3 ：$\angle DOA = 360^\circ - \angle AOD - \angle DAO = 360^\circ - 120^\circ - 135^\circ = 105^\circ$