Question

Tan
Part A
What is the measure, in degrees, of ZPTR? Enter your answer in the bo

Answer 1

`\purple {\bold {m\angle PTR=136\degree}}`

`\orange {\bold {m\angle PQR=68\degree}}`

Explanation:

PS and RS are tangents to the circle with center T at points P and R. (given)

TP and TR are radii of the given circle.

`\therefore PS\perp TP\: \&\: RS\perp TR`

(radius is perpendicular to the tangent)

`\therefore m\angle TPQ= m\angle TRS =90\degree`

In quadrilateral SPTR

`m\angle TPQ+ m\angle TRS+m\angle PSR +m\angle PTR=360\degree`

`90\degree+ 90\degree+44\degree +m\angle PTR=360\degree`

`224\degree +m\angle PTR=360\degree`

`m\angle PTR=360\degree - 224\degree`

`\purple {\bold {m\angle PTR=136\degree}}`

By inscribed angle theorem:

`m\angle PQR=(1)/(2) * m\angle PTR`

`m\angle PQR=(1)/(2) * 136\degree`

`\orange {\bold {m\angle PQR=68\degree}}`