Question

In fig. the values of x and y are equal to
(a) 130° (b) 150
c) 160
(d) 135​

Answer 1

Answer:

x+50=180=[180]

x=180-50

x=130 Also =Vertically opposite angles

x+y=130(alternate interior angles)

Answer 2

Given,

$\[\begin{array}{l}\angle AXL = 50^\circ \\\angle x = ?\\\angle y = ?\end{array}\]$

Solution,

Observe the figure, $\[AB\parallel CD\]$.

If a straight line cut by another line then the sum of angles on the straight line will be $\[180^\circ \]$.

AB line cut by straight line l.

$\[\begin{array}{l}\angle x + \angle AXL = 180^\circ \\ \Rightarrow \angle x + 50^\circ = 180^\circ \\ \Rightarrow \angle x = 130^\circ \end{array}\]$

Angle x and angle y both are alternate interior angles.

$\[\begin{array}{l}\angle y = \angle x\\ \Rightarrow \angle y = 130^\circ \end{array}\]$

Hence the values of x and y are $\[\ 130^\circ \end{array}\]$

The correct option is (a), i.e. $\[130^\circ \]$