Question

please solve it emergeny i will mark you brainlist

Answer 1

$<b> <tt>$
we know the sum of angles of a triangle is equal to 180°.

Given:
$\angle \: PQS = 50° and \: \angle \: PRT = 30° \\ \\ \tt{we \: also \: know \: that \: PT \: is \: a \: bisector } \\ \tt{ of \angle \: PQR}$

In ∆ PQR.

$\angle \: PQS+ \angle \: PRT + \angle \: PQR = 180° \\ \\ \rightarrow50° + 30° + \angle \: PQR \: = 180° \\ \\ \rightarrow80° + \angle \: PQR = 180° \\ \\ \rightarrow \angle \: PQR \: = 180° - 80° \\ \\ \rightarrow\angle \: PQR \: = 100°$
then, we know the PT is a angle bisector angle PQR.

so, it divides the angle into Half's.

$=> \angle \: RPT + \angle \: TPQ = 100 \\ \\ we \: can \: consider \: them \: be \: x \\ \\ => x + x =100 \\ \\ => 2X= 100 \\ \\ => X = \frac{100}{2} . \\ \\ = > x = 50.$

now, In ∆ PQT

PS is the bisector of angle QPT .it divides the angle into to half then,

we know angle QPT is equal to 50.

now,

$\angle QPS + \angle \: SPT = \angle \: QPT \\ \\ \rightarrow \:\angle QPS + \angle \: SPT \: = 50 \\ \\ \tiny \tt{let \: them \: both \: be \: x \: beocz \:PS \: is \: bisector \angle \: QPT.}\: \\ \\ \rightarrow x + x = 50 \\ \\ \rightarrow2x = 50 \\ \\ \rightarrow x = \frac{50}{2} \\ \\ \rightarrow \: x = 25. \\ \\ so. \angle \: SPT = 25 \: \: \red{\underline {\underline{{ \tt{solved}}}}}$