Question

find the value of X and y​

Answer 1

ANSWER✔

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

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

$\sf\dashrightarrow ABCD\:is \: quadrilateral$

$\sf\dashrightarrow \angle DAB=102 \degree$

$\sf\dashrightarrow \angle DCB=95 \degree$

$\sf\dashrightarrow \angle CBE=120 \degree$

$\sf\dashrightarrow \angle ABC=y \degree$

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

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

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

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

$\sf\therefore \text{finding the value of angle y}$

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

$\sf\dashrightarrow \angle ABC+ \angle CBE= 180\degree$

$\sf\implies y\degree+120\degree=180\degree$

$\sf\implies y= 180-120$

$\sf\dashrightarrow y= 60\degree$

$\large{\boxed{\bf{ \star\:\: \angle y= 60\degree\:\: \star}}}$

$\green{\text{BISECTING A QUADRILATERAL ABCD IN TWO PARTS OF A TRIANGLE, }}$

$\sf\therefore \triangle ADB \:and\: \triangle CDB$

$\sf\star \: \angle ABD = \angle BCD = \dfrac{1}{2}\: \angle BDC$

$\sf\dashrightarrow \angle ABD = \angle BCD = \dfrac{1}{2}\times (60)\degree$

$\sf\dashrightarrow \angle ABD = \angle BCD = 30\degree$

$\bf\therefore \: \angle ADC= \angle ADB + \angle BDC$

$\sf\therefore in \triangle ADB,$

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

$\sf\dashrightarrow \angle ADB + \angle DAB + \angle ABC= 180 \degree$

$\sf\implies \angle ADB+102+30=180\degree$

$\sf\implies \angle ADB +132=180\degree$

$\sf\implies \angle ADB= 180-132$

$\sf\implies \angle ADB= 48\degree$

$\sf\therefore in \triangle CDB,$

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

$\sf\dashrightarrow \angle CDB + \angle DBC + \angle DCB= 180 \degree$

$\sf\implies \angle CDB + 30+95=180\degree$

$\sf\implies \angle CDB +125=180$

$\sf\implies \angle CDB= 180-125$

$\sf\implies \angle CDB= 55\degree$

$\bf\therefore \: \angle ADC= \angle ADB + \angle BDC$

$\sf\dashrightarrow 48\degree + 55\degree$

$\sf\implies \angle ADC=103\degree$

$\sf\therefore \text{finding the value of angle x}$

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

$\sf\dashrightarrow \angle FDA + \angle ADC=180\degree$

$\sf\implies \angle x+103=180\degree$

$\sf\implies x=180-103$

$\sf\implies x=77\degree$

$\large{\boxed{\bf{ \star\:\: x=77\degree \:\: \star}}}$

$\large\underline\bold{THE\:VALUE\:OF\:y\:IS\:60\degree}$

$\large\underline\bold{THE\:VALUE\:OF\:x\:IS\:77\degree}$

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