Question

Find unknown angle in parallelogram in which one angle is 75 degree

Answer 1

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Answer 2

$\mathbb{ SOLUTION }$:

$\angle{S}$ = $\angle{Q}$
[ $\therefore$ Opposite angles of parallelogram are equal ]
so,
if $\angle{S}$ = 75°
then, $\angle{Q}$ = 75°

PQ ll SR and PS ll QR

$\angle{P}$ + $\angle{S}$ = 180°
[ $\therefore$ Supplementary angles ]
$\angle{P}$ + 75° = 180°
$\angle{P}$ = 180° - 75°
$\angle{P}$ = 105°

Now,
$\angle{P}$ = $\angle{R}$
[ $\therefore$ Opposite angles of parallelogram are equal ]
$\angle{R}$ = 105°

Hence,
$\angle{P}$ = 105°
$\angle{Q}$ = 75°
$\angle{R}$ = 105°
$\angle{S}$ = 75°