Question

The figure shows secants PS and PT and tangent QR intersecting at point P. Triangle STP is an isosceles triangle with legs PS and PT find x and y

Answer 1

x°=70° and y°=40°

Explanation:

We are given that secants PS and PT and tangent QR intersecting at point P. Triangle STP is an isosceles triangle with legs PS and PT.

Now, we know that
`Inscribed angle=(1)/(2)intercepted arc`, thus

⇒2m∠PST=m(TP)

⇒2m∠PST=140°

⇒m∠PST=70°

Since, the ΔPST is an isosceles triangle with SP=TP, therefore

∠PST=∠PTS=70°

Now,in ΔPST, applying the angle sum property, we have

∠PST+∠PTS+∠SPT=180°

⇒70°+70°+∠SPT=180°

⇒140°+∠SPT=180°

⇒∠SPT=180°-140°

⇒∠SPT=40°

therefore, y°=40°

Now, using the theorem that angle made with the tangent is equal to the interior angle of the inscibed triangle, thus

x°=∠PTS

⇒x°=70°

Thus, the value of x and y is: 70 and 40 respectively.

Answer 2

I hope this helps you