Question

how angle PQR is 36 ? explain step by step please​

Answer 1

Answer:

Given−

PQisadiameterofacirclewithcentreO.

PTisatangenttothecirclefromTatP.

QTintersectsthecircleatR.

∠POR=72°

.

To find out−

∠PTR=?

Solution−

The diameter PQ orthe radius OP meets the tangent PT at P.

∴PQ⊥PTsince be the radius through the point of contact of

a tangent to a circle is perpendicular to the tangent.

∴∠QPT=90°

Again the minor arc PR subtends ∠POR to the centre O

and∠PQR to the cicumference.∴∠PQR= 1/2×∠POR= 1/2 ×72 =36

.

So in ΔPQT

∠QTP=180 °

−(∠PQR+∠QPT) (by angle sum property of triangles) =180 °−(36 ° +90 ° )=54 °

Step-by-step explanation:

hope it will help you