Question

Find x in the following figure ​

Answer 1

ANSWER✔

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

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

$\dashrightarrow \: \angle ABC= 40\degree$

$\dashrightarrow \angle DAC= 45\degree$

$\dashrightarrow \angle ADC= 90\degree$

$\dashrightarrow \angle ACD= y\degree$

$\dashrightarrow \angle ABD=x\degree$

$\dashrightarrow \angle ADC= 90\degree \:--\boxed{ \angle ADC = \angle ADB \:[ as\:AD \:is\:perpendicular\:to\:BC}$

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

$\dashrightarrow Value\:of\:x$

✯.IDENTITY IN USE,

$\large{\boxed{\bf{ \star\:\: \:angle\:sum\:property\:of\:triangle=180\degree\:\: \star}}}$

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

$\therefore \:finding\:the\:value\:of\:x,$

$\sf\large\therefore in\: \triangle ABD,$

$\dashrightarrow \angle ABD+ \angle BDA + \angle DAB =180\degree$

$\implies 40 + 90+ x= 180\degree$

$\implies 130\degree+x=180\degree$

$\implies x=180-130$

$\implies x=50\degree$

$\large{\boxed{\bf{ \star\:\: \angle BAD(x)= 50\degree \:\: \star}}}$

$\therefore \:finding\:the\:value\:of\:y,$

$\sf\large\therefore in\: \triangle ADC,$

$\dashrightarrow \angle DAC= 45\degree$

$\dashrightarrow \angle ADC= 90\degree$

$\therefore by\:angle\:sum\:property,$

$\dashrightarrow \angle ADC+ \angle DAC + \angle ACD =180\degree$

$\implies 90+45+y=180\degree$

$\implies 135+y= 180$

$\implies y= 180-135$

$\implies y=45\degree$

$\large{\boxed{\bf{ \star\:\: \angle ACD (y)=45\degree\:\: \star}}}$

$\large\underline\bold{VALUE\:OF\:x\:IS\:50\degree\:AND\:VALUE\:OF\:y\:IS\:45\degree}$

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