Question

In the figure, two parallel lines l and m are cut by two transversals n and p. Then the values of x and y are:

• A. $x={114}^{\circ }$
• B. $x={132}^{\circ }$
• C. $y={132}^{\circ }$
• D. $y={114}^{\circ }$

Answer 1

Answer: (A), (C)

The correct options are
A $x={114}^{\circ }$
C $y={132}^{\circ }$

Since l || m and p is a transversal line,
$x+{66}^{\circ }={180}^{\circ }$ (sum of angles on same side of transversal is supplementary)
Or, $x={180}^{\circ }-{66}^{\circ }$
$={114}^{\circ }$
Again, l || m and n is a transversal line.
$\therefore y+{48}^{\circ }={180}^{\circ }$
$\therefore y={180}^{\circ }-{48}^{\circ }={132}^{\circ }$