Question

Question 90

Iron rods a, b, c, d, e and f are making a design in a bridge as shown in the given figure, in which a || b, c|| d and e || f. Find the marked angles between
(i) b and c
(ii) d and e
(iii) d and f
(iv) c and f

Answer 1

Since l, m are two parallel lines and PQ, RS and TU are transversal.
Then, $\angle 4=\angle QPS\left[alternateinteriorangles\right]\Rightarrow \angle 4={75}^{\circ }[\therefore \angle QPS={75}^{\circ }]$
Again, $\angle 1=\angle QOR\left[verticallyoppositeangles\right]\Rightarrow \angle 1={30}^{\circ }[\therefore \angle QOR={30}^{\circ }]$
Also, PQ and TU are parallel and m and l are transversal.
Therefore, $\angle 2+\angle QPT={180}^{\circ }\left[consecutiveinteriorangles\right]\Rightarrow \angle 2={180}^{\circ }-{75}^{\circ }[\therefore \angle QPT={75}^{\circ },given]\Rightarrow \angle 2={105}^{\circ }$
Also, $\angle 2+\angle 3={180}^{\circ }\Rightarrow {105}^{\circ }+\angle 3={180}^{\circ }\Rightarrow \angle 3={180}^{\circ }-{105}^{\circ }\Rightarrow \angle 3={75}^{\circ }$
Hence (i) ${30}^{\circ }$ (ii) ${105}^{\circ }$
(iii) ${75}^{\circ }$ (iv) ${75}^{\circ }$