Question

Find
the
values
of

x
and
y​

Answer 1

Answer:

i-x=30

y=100

ii-x=110

y=70

Step-by-step explanation:

i-x+50=80

=>x=80-50=30

y=180-30-50=180-80=100

ii-x=50+60=110

y=180-x=180-110=70

Answer 2

$\sf \dag \: Given \begin{cases} \sf (i) Two \: angles \: of \: the \: triangle \: i.e \: 50^{\circ} and \: 80^{\circ} \\ \\ \sf (ii) Two \: angles \: of \: the \: triangle \: i.e \: 50^{\circ} and \: 60^{\circ}\end{cases}$

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Need to find: The values of x & y in both ?

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❍ As vertically opposite angles are equal, y = 80°.(i)

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As we know that,

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$\begin{gathered}\star\:{\underline{\boxed{\frak{(i) \: Sum \: of \: all \: angles \: of \: a \: triangle = 180^{\circ}}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{Putting\:given\:values\:in\:formula,}}}\\\\\\ :\implies\sf 80 ^{ \circ}+ 50x ^{ \circ} + x = 180 ^{ \circ} \\\\\\ :\implies\sf 130^{ \circ} + x = 180^{ \circ} \\\\\\ :\implies\sf x = 180^{ \circ} -130^{ \circ} \\\\\\ :\implies{\underline{\boxed{\frak{\purple{x =50^{ \circ}}}}}}\:\bigstar\\\\\end{gathered}$

$\begin{gathered}\star\:{\underline{\boxed{\frak{(ii) \: Sum \: of \: all \: angles \: of \: a \: triangle = 180^{\circ}}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{Putting\:given\:values\:in\:formula,}}}\\\\\\ :\implies\sf 60^{ \circ}+ 50^{ \circ} + y = 180 ^{ \circ} \\\\\\ :\implies\sf 110^{ \circ} + y = 180^{ \circ} \\\\\\ :\implies\sf y = 180^{ \circ} -110^{ \circ} \\\\\\ :\implies{\underline{\boxed{\frak{\purple{y =70^{ \circ}}}}}}\:\bigstar\\\\\end{gathered}$

Now, x :

$\begin{gathered}\star\:{\underline{\boxed{\frak{180^{ \circ} - y = x}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{Putting\:given\:values\:in\:formula,}}}\\\\\\ :\implies\sf 180 ^{ \circ} - 70^{ \circ}\\\\\\ :\implies{\underline{\boxed{\frak{\purple{y =110^{ \circ}}}}}}\:\bigstar\\\\\end{gathered}$

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Therefore,

(i) y = 80°, x = 50°

(ii) y = 70° , x = 110°.

$\therefore\:{\underline{\sf{ The\:value\:x\:and\:y\:in \: (i) \: and \: (ii) \: is \: \bf{(i)y = 80°, x = 50^\circ}}\: \sf{and}\: \bf{(ii) y = 70^\circ , x = 110^\circ\sf{respectively}.}}}$