Question

In Fig., if $ST=SU$, then find the values of $x$ and $y$.

Answer 1

We have

$\angle TSU={78}^o$ [vertically opposite angles]

Given,

$TS=US$

$\Rightarrow \angle SUT=\angle STU=y$

Now, in $△STU$

$\angle SUT+\angle STU+\angle TSU={180}^o$

$\Rightarrow y+y+{78}^o={180}^o$

$\Rightarrow 2y={180}^o-{78}^o$

$\Rightarrow y=\frac{{102}^o}{2}$

$\Rightarrow y={51}^o$

Now, by exterior angle property,

$x=\angle TSU+\angle UTS$

$\Rightarrow x={78}^o+{51}^o$

$\Rightarrow x={129}^o$

Hence $x={129}^o$ and $y={51}^o$