Mathematics

# 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 .

##### SOLUTION
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)
$\Rightarrow \angle c = \angle b = 45^\circ$

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Subjective Medium Published on 09th 09, 2020
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