Question

Three angles are 45 degree, 75 degree and 105 degree. Find the 4th angle​

Answer 1

The three angles of the quadrilateral = 45,75,105

4th angle of the quadrilateral = let 'x'

sum of all angles in a quadrilateral = 360

$45 + 75 + 105 + x = 360 \\ 225 + x = 360 \\ x = 225 - 360 \\ x = 135$

Answer 2

Given :-

• Three angles are 45° , 75°, and 105°.

To find :-

• The fourth angle

Solution :-

${ \tt{let \: the \: fourth \: angle \: be \: x}} \\ \\ {45}^{o} + {75}^{o} + {105}^{o} + x = {360}^{o} \: \: \: \: \pink{ \mathfrak{sum \: of \: all \: angles \: in \: a \: quadrilateral \: is \: {360}^{o} }} \\ {120}^{o} + {105}^{o} + x= {360}^{o} \\ x = {135}^{o}$

$\red{ \tt{hence \: the \: fourth \: angle \: is \: of \: {135}^{o} }}$

$\dag \: \large\pink{ \mathfrak{formula \: used }} \: \dag \\ \implies{ \tt{sum \: of \: all \: angles \: in \: a \: quadrilateral \: is \: {360}^{o} }}$

HOPE IT HELPS YOU!