Question

In Fig. 72, if AB || CD and AE || BD, then the value of x is

(a) 38
(b) 48
(c) 58
(d) 68

Answer 1

In the given figure,
$$\begin{gathered} \mathrm{AE}\parallel \mathrm{BD}\left(\mathrm{given}\right) \\ \Rightarrow \angle \mathrm{A}+\angle \mathrm{B}={180}^{\circ }\left(\mathrm{co}-\mathrm{interior}\mathrm{angles}\right) \end{gathered}$$
Sum of all the angles of a polygon is given by $\left(n-2\right)\times {180}^{°}$, where n is the number of sides of the polygon.
The given polygon has number of sides(n) = 5
So, sum of all the angles = $\left(n-2\right)\times {180}^{°}=\left(5-2\right)\times {180}^{°}=3\times {180}^{°}={540}^{°}$
$$\begin{gathered} \Rightarrow \angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}+\angle \mathrm{E}={540}^{°} \\ \Rightarrow 180°+132°+84°+3x=540°\left(\mathrm{since},\angle \mathrm{A}+\angle \mathrm{B}=180°\right) \\ \Rightarrow 3x+396°=540° \\ \Rightarrow 3x=540°-396°=144° \end{gathered}$$
Divide both sides by 3, we get
$x=48°$