Question

In the given figure, find the value of ∠BAE. [3 Marks]

Answer 1

Sum of inner angles of a pentagon
$=(n-2)\times {180}^0$
$=(5-2)\times {180}^0={540}^0$ [1 Mark]
$x^0+(x+20{)}^0+(x+20{)}^0+(x+40{)}^0+(x+40{)}^0={540}^0$
$\Rightarrow 5x+{120}^0={540}^0$ [1 Mark]
$\Rightarrow x=\frac{{420}^0}{5}$
$\Rightarrow x={84}^0$
$\therefore \angle BAE={84}^0$ [1 Mark]