Question

find the value of X and y in following diagrams​

Answer 1

★ How to do :-

Here, we are given with a triangle which has an other exterior angle. The measures of two interior angles are given. The two angles are named as x and y, which is needed to be found. Here, we are going to use the concepts of linear pair of angles, triangle dum property and also the exterior angle property. These are the concepts which are used to find the measurements of many angles in a triangle. First let's find the value of x and then later we can find the value of y. So, let's solve!!

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➤ Solution :-

To find the value of 'x' we are going to use the concept of exterior angle property. Let's solve.

Value of 'x' :-

${\sf \leadsto exterior \: angle = sum \: of \: opposite \: interior \: angles}$

${\tt \leadsto x = 50 + 60}$

${\tt \leadsto \boxed{\tt \orange{x = {110}^{\circ}}}}$

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Value of 'y' :-

To find the value of 'y' we are going to use the concept of triangle sum property. Let's solve.

${\sf \leadsto sum \: of \: all \: angles = 180}$

${\tt \leadsto y + 50 + 60 = 180}$

${\tt \leadsto y + 110 = 180}$

${\tt \leadsto y = 180 - 110}$

${\tt \leadsto \boxed{\tt \orange{y = {70}^{\circ}}}}$

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Verification :-

${\tt \leadsto \angle{x} + \angle{y} = {180}^{\circ}}$

${\tt \leadsto 110 + 170 = {180}^{\circ}}$

${\tt \leadsto {180}^{\circ} = {180}^{\circ}}$

Hence verified !!

Answer 2

∠x=110°

∠y=70°

Step-by-step explanation:

Solution -

‎ ‎

➠ㅤLet's first find the value of ∠y.

$y + 50° + 60° = 180°$

$\small\color{black}\boxed{\colorbox{saffron}{Angle\:Sum\:Property=180°}}$

$y + 110° = 180° \\ \\ y = 180 - 110 \\ \\ y = 70°$

So, ∠y=70°

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➠ㅤNow, let's find the value of ∠x.

$x=50°+60°$

$\color{black}\small\boxed{\colorbox{saffron}{Exterior\:Angle\:Property=sum\:of\ :first\:2\:sides}}$

$x=110°$

So, ∠x=110°

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Verification -

$∠y+∠x=180°$

$\color{black}\boxed{\colorbox{saffron}{sum\:of\:linear\:pairs=180°}}$

$70°+110°=180°\\ \\180°=180°$

Hence proved!