Question
Find the values of $x$ and $y$ in Figure.
✓
Answer
In $\triangle\text{TQS},$
$\Rightarrow\angle\text{T}+\angle\text{Q}+\angle\text{S}=180^{\circ} [$angle sum property of a triangle$]$
$\Rightarrow \ 50^{\circ}+30^{\circ}+\angle1=180^{\circ}$
$\Rightarrow \ 80^{\circ}+\angle1=180^{\circ}$
$\Rightarrow \ \angle1=180^{\circ}- 80^{\circ}=100^{\circ}$
Now, $\angle1+\text{x}=180^{\circ}$ [linear pair]
$\Rightarrow100^{\circ}+\text{x}=180^{\circ}=180^{\circ}-100^{\circ}$
$\Rightarrow \ \text{x}=80^{\circ}$ In $\triangle\text{TSR},$
$\text{x}+45^{\circ}+\angle\text{2}=180^{\circ}[$angle sum propery of a triangle$]$
$\Rightarrow\angle2=180^{\circ}-80^{\circ}-45^{\circ}=55^{\circ}$
Now, $50^{\circ}+\angle2+\text{y}=180^{\circ} [$linear pair$]$
$\Rightarrow\text{y}=180^{\circ}-50^{\circ}-55^{\circ}=75^{\circ}$
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