a) Show that $∠ D O A = 105^{\circ}$
b) Show that the length of DA is $127 m$ (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

$∠ D O A = 360^{\circ} - ∠ A O D - ∠ D A O = 360^{\circ} - 120^{\circ} - 135^{\circ} = 105^{\circ}$

Steps

Step 1 ： $∠ A O C = 180^{\circ} - ∠ B O C = 180^{\circ} - 120^{\circ} = 60^{\circ}$

Step 2 ： $∠ A O D = 180^{\circ} - ∠ A O C = 180^{\circ} - 60^{\circ} = 120^{\circ}$

Step 3 ： $∠ D O A = 360^{\circ} - ∠ A O D - ∠ D A O = 360^{\circ} - 120^{\circ} - 135^{\circ} = 105^{\circ}$