Question

Question 149
In parallelogram FIST, find $\angle SFT,\angle OST$ and $\angle STO$.

Answer 1

Given, $\angle FIS={60}^{\circ }$
Now, $\angle FTS=\angle FIS={60}^{\circ }$ [$\because$ opposite angles of a parallelogram are equal]
Now, $FT\parallel IS$ and TI is a transversal, therefore $\angle FIO=\angle STO={35}^{\circ }$ [alternate angles]

Also, $\angle FOT+\angle SOT={180}^{\circ }$ [linear pair]
$\Rightarrow {110}^{\circ }+\angle SOT={180}^{\circ }$
$\Rightarrow \angle SOT={70}^{\circ }$
In $\Delta TOS,\angle TSO+\angle OTS+\angle TOS={180}^{\circ }$ [angle sum property of triangle]
$\therefore \angle OST={180}^{\circ }-({70}^{\circ }+{35}^{\circ })={75}^{\circ }$

In $\Delta FST,\angle SFT+\angle FTS+\angle TSF={180}^{\circ }$ [angle sum property of triangle]
$\Rightarrow \angle SFT={180}^{\circ }-({60}^{\circ }+{75}^{\circ })\therefore \angle SFT={45}^{\circ }$