Question

In the given figure, line l || line m and line n || p . Find $\angle a,\angle b,\angle c.$ from the given measure of an angle .

Answer 1

Let us mark the points R and S on line n, T and U on line p, A and B on line l and C and D on line m.

Suppose the lines n and p intersect the line l at K and L respectively and line m at M and N respectively.

Since, the line l and line p intersect at L, then

$\angle KLN=\angle BLT$ (Vertically opposite angles)

$\Rightarrow \angle KLN={45}^{\circ }$

Since, line l $\parallel$ line m and line p is a transversal intersecting them at L and N, then

$\angle KLN+\angle MNL={180}^{\circ }$ (Pair of interior angles on the same side of transversal is supplementary)

$\Rightarrow {45}^{\circ }+\angle a={180}^{\circ }$

$\Rightarrow \angle a={180}^{\circ }-{45}^{\circ }={135}^{\circ }$

Since, the line m and line p intersect at N, then

$\angle DNU=\angle MNL$ (Vertically opposite angles)

$\Rightarrow \angle b=\angle a={135}^{\circ }$

Since, line n $\parallel$ line p and line m is a transversal intersecting them at M and N, then

$\angle NMS=\angle DNU$ (Corresponding angles)

$\Rightarrow \angle c=\angle b={135}^{\circ }$