Question

find the measure of angle c​

Answer 1

Step-by-step explanation:

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Answer 2

Given : In a Quadrilateral ABCD , ∠A = 45⁰ , ∠B = 135⁰ and ∠C = ∠D .

Need to Find : The measure of the ∠C and ∠D

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$\sf{\bf{ Solution \:of\:Question \::}}$ Let's consider ∠C of Quadrilateral be x⁰ .

Given that ,

⠀⠀⠀⠀⠀⠀⠀⠀∠C of Quadrilateral = ∠D of Quadrilateral

⠀⠀⠀⠀⠀As , We have consider ∠C as , x⁰ .

Then ,

⠀⠀⠀⠀⠀∠D = x⁰

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⠀⠀⠀⠀⠀We know that if we know two angles ( ∠A & ∠B ) of Quadrilateral and we have already assumed ∠C and with the help of ∠C we have found the ∠D . And now we know Values of all angles of Quadrilateral . And now for exact measure of ∠C and ∠D of Quadrilateral we need the sum of all four angles of Quadrilateral that is :

⠀⠀⠀⠀⠀$\implies {\underline {\mathrm {\red{The\:sum\:of\;all\:angles \:of\:Quadrilateral \:is\:360\degree}}}}$

⠀⠀⠀⠀⠀$\implies {\underline {\mathrm {\red{\angle A + \angle B + \angle C + \angle D = \:360\degree}}}}$

⠀⠀⠀⠀⠀Here ∠A is the First angle of Quadrilateral, ∠B is the second angle of Quadrilateral, ∠C is the Third angle of Quadrilateral & ∠D is the Fourth angle of Quadrilateral and we already know that all angles of Quadrilateral. And First Angle ( ∠A ) = 45⁰ , Second Angle (∠B) = 135⁰ , Third Angle (∠C) = x⁰ & Fourth Angle (∠D) = x⁰ . So , By using known Values we can find the value of 'x' :

⠀⠀⠀⠀⠀$\sf{\underline {\bf{ \star { Now \: By \:Substituting \;Know \:Values \::}}}}$

⠀⠀⠀⠀⠀$\longmapsto { \mathrm { 135 + 45 + x + x = 360\degree }}$

⠀⠀⠀⠀⠀$\longmapsto { \mathrm { 135 + 45 + 2x = 360\degree }}$

⠀⠀⠀⠀⠀$\longmapsto { \mathrm { 180 + 2x = 360\degree }}$

⠀⠀⠀⠀⠀$\longmapsto { \mathrm { 2x = 360 - 145 }}$

⠀⠀⠀⠀⠀$\longmapsto { \mathrm { 2x = 180\degree }}$

⠀⠀⠀⠀⠀$\longmapsto { \mathrm { x =\dfrac {\cancel {180}}{{2}} }}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm { x = 90\degree \: }}}}$

Therefore,

• ∠C or Third Angle = x = 90⁰

• ∠D or Fourth Angle = x = 90⁰

Therefore,

⠀⠀⠀⠀⠀$\underline {\therefore\:{\pink{ \mathrm { Hence,\:The\:measure \:of\:\angle C \:(Third \:Angle)\: and\:\angle D ( Fourth \: Angle )}}}}\\\sf{\underline {\pink{\:of\: Quadrilateral \:are\: 90\degree\:and\:90\degree\:,respectively. }}}$

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Verification :

As , We know that ,

⠀⠀⠀⠀⠀$\longmapsto { \mathrm { L.H.S\: =\: Sum\:of\:Angle \:of\:Quadrilateral =\: 360\degree }}$

⠀⠀⠀⠀⠀$\sf{\underline {\bf{ \star { Now \: By \:Finding \:R.H.S \:using\:known\:and\:found\:values\::}}}}$

⠀⠀⠀⠀⠀$\longmapsto { \mathrm { R.H.S = 135 + 45 + 90 + 90 }}$

⠀⠀⠀⠀⠀$\longmapsto { \mathrm { R.H.S = 180 + 90 + 90 }}$

⠀⠀⠀⠀$\longmapsto { \mathrm { R.H.S = 180 + 180 }}$

⠀⠀⠀⠀$\longmapsto { \mathrm { R.H.S = 360\degree }}$

Therefore,

⠀⠀⠀⠀$\longmapsto { \mathrm { L.H.S = R.H.S }}$

⠀⠀⠀⠀$\dag { \mathrm{\bf { Hence ,\:Verified\: !} }}$

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