Question

please answer this question with showing all the workings if you know the answer then only answer else reported answer correctly​

Answer 1

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow \angle FEG= 90\degree$

$\sf\dashrightarrow \angle GAB = \angle 1$

$\sf\dashrightarrow \angle HBC =40\degree$

$\sf\dashrightarrow \angle ICD= x\degree$

$\sf\dashrightarrow \angle JDE= 60\degree$

$\sf\dashrightarrow \angle EAB = 90\degree$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow\text{ the value of angle 1 and x}$

✯.PROPERTY IN USE,

$\bf{\boxed{\bf{ \star\:\: SUM\:OF\:EXTERIOR\:ANGLES\:OF\: QUADRILATERAL=360\degree\:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\sf\dashrightarrow \text{ first finding the value of angle 1,}$

$\sf\therefore\text{ by angle sum property,}$

$\sf\dashrightarrow \angle GAB +\angle EAB=180\degree$

$\sf\implies \angle 1+ 90\degree=180\degree$

$\sf\implies \angle 1 =180-90$

$\sf\implies \angle 1= 90\degree$

$\large{\boxed{\bf{ \star\:\:\angle 1= 90\degree \:\: \star}}}$

$\sf\star \:\: \text{ Now, finding the value of x,}$

$\sf\therefore SUM\:OF\:EXTERIOR\:ANGLES\:OF\: QUADRILATERAL=360\degree$

$\sf\dashrightarrow \angle FEG+ \angle GAB + \angle HBC + \angle ICD+ \angle JDE=360\degree$

$\sf\implies 90\degree + 90\degree + 40\degree +x +60\degree=360\degree$

$\sf\implies 180\degree+100\degree = 360\degree$

$\sf\implies 280\degree+ x=360\degree$

$\sf\implies x=360-280$

$\sf\implies x= 80\degree$

$\large{\boxed{\bf{ \star\:x= 80\degree \:\: \star}}}$

$\large\underline\bold{THE\:VALUE\:OF\:\angle 1\:IS\:90\degree }$

$\large\underline\bold{THE\:VALUE\:OF\:\angle ICD \:IS\:80\degree}$

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$\red{\text{NOTE:- PLEASE REFER THE ATTACHMENT.}}$

Answer 2

${\tt{\purple{\underline{\underline{\huge{Answer:}}}}}}$

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow \angle FEG= 90\degree$

$\sf\dashrightarrow \angle GAB = \angle 1$

$\sf\dashrightarrow \angle HBC =40\degree$

$\sf\dashrightarrow \angle ICD= x\degree$

$\sf\dashrightarrow \angle JDE= 60\degree$

$\sf\dashrightarrow \angle EAB = 90\degree$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow\text{ the value of angle 1 and x}$

.PROPERTY,

$\bf{\boxed{\bf{ \:\: SUM\:OF\:EXTERIOR\:ANGLES\:OF\: QUADRILATERAL=360\degree\:\: }}}$

$\large\underline\bold{SOLUTION,}$

$\sf\dashrightarrow \text{ first finding the value of angle 1,}$

$\sf\therefore\text{ by angle sum property,}$

$\sf\dashrightarrow \angle GAB +\angle EAB=180\degree$

$\sf\implies \angle 1+ 90\degree=180\degree$

$\sf\implies \angle 1 =180-90$

$\sf\implies \angle 1= 90\degree$

$\large{\boxed{\bf{ \star\:\:\angle 1= 90\degree \:\: \star}}}$

$\sf\star \:\: \text{ Now, finding the value of x,}$

$\sf\therefore SUM\:OF\:EXTERIOR\:ANGLES\:OF\: QUADRILATErAL=360\degree$

$\sf\dashrightarrow \angle FEG+ \angle GAB + \angle HBC + \angle ICD+ \angle JDE=360\degree$

$\sf\implies 90\degree + 90\degree + 40\degree +x +60\degree=360\degree$

$\sf\implies 180\degree+100\degree = 360\degree$

$\sf\implies 280\degree+ x=360\degree$

$\sf\implies x=360-280$

$\sf\implies x= 80\degree$

$\large{\boxed{\bf{ \:\:x= 80\degree \:\: }}}$

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