Question

find the value of x​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\bold{Given:-}\begin{cases}\sf{A\: quadrilateral\:in\: which}\\ \sf{ \angle DAB=75{}^{\circ}}\\ \sf{Exterior\:angles =85{}^{\circ}\:\:and\:105{}^{\circ}}\end{cases}$

$\huge\sf{\red{To\:Find:-}}$

• We have to find the value of x

$\bf\underline{\underline{According\:To\: Question:-}}$

• First find the two interior angles of quadrilateral

$\sf \angle ABC=180{}^{\circ}-85{}^{\circ}\:\:(Linear\: pair)\\ \\ \sf\implies \angle ABC=95{}^{\circ}$

$\boxed{\tt{\purple{ \angle ABC=95{}^{\circ}}}}$

• Now find the value of angle DCB

$\sf \implies \angle BCD=180{}^{\circ}-110{}^{\circ}\:\:(Linear\: pair)\\ \\ \sf\implies \angle BCD=70{}^{\circ}$

$\boxed{\tt{\purple{ \angle BCD=70{}^{\circ}}}}$

• Now the value of x

• First find angle ADC

$\boxed{\rm{\red{ \angle ADC+\angle DAB+\angle ABC+\angle BCD=360{}^{\circ}}}}$

$\sf\implies \angle ADC=360{}^{\circ}-75{}^{\circ}-95{}^{\circ}-70{}^{\circ}\\ \\ \sf\implies \angle ADC=360{}^{\circ}-240{}^{\circ}\\ \\ \sf\implies \angle ADC=120{}^{\circ}$

$\boxed{\tt{\purple{\angle ADC=120{}^{\circ}}}}$

• Now the value of x

$\sf\implies \angle ADC+x=180{}^{\circ}\:\:\: (Lines\:pair)\\ \\ \sf\implies 120{}^{\circ}+x=180{}^{\circ}\\ \\ \sf\implies x=180{}^{\circ}-120{}^{\circ}\\ \\ \sf\implies \angle ADC=60{}^{\circ}$

$\huge\underline{\boxed{\mathfrak{\star{x=60{}^{\circ}}}}}$

#BAL

#answerwithquality