Question

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

Answer 1

Answer:

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

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

Step-by-step 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:

$m\angle PQR=\frac{1}{2} \times m\angle PTR$

$m\angle PQR=\frac{1}{2} \times 136\degree$

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