Question

if PS/QS=PT/TR and pST=70, QpR=50 then QRP =?​

Answer 1

Step-by-step explanation:

Hello this for you

Answer 2

Given:

$\frac{PS}{QS}=\frac{PT}{TR}$

∠PST = 70°

∠QPR = 50°

To find:

The measure of ∠QRP.

Solution:

Let PQR be a triangle. Consider a line ST that intersects the two sides PQ and PR of the triangle proportionally such that $\frac{PS}{QS}=\frac{PT}{TR}$ which is given in the problem. Hence, by the converse of triangle proportionality theorem, we can say that line ST is parallel to the third side of the triangle, QR.

Since ST is parallel to QR and PQ is the transversal to these parallel lines, then the corresponding angles are equal, i.e,

∠PST = ∠PQR

∠PST = 70°

∴ ∠PQR = 70°

In ΔPQR,

∠PQR = 70°, ∠QPR = 50°

By angle sum property of triangle, sum of all angles in a triangle equate to 180°.

∠PQR + ∠QPR + ∠QRP = 180°

$70+50$ + ∠QRP = $180$

$120$ + ∠QRP = $180$

∠QRP = $180-120=60^{0}$

Hence, the measure of ∠QRP is 60°.

The measure of ∠QRP is 60°.