Question

Circle T is shown. Line segments P R and Q S are diameters. Lines are drawn to connect point P and point Q and point S and point R to form 2 triangles. Angle P Q T is 40 degrees. Line P R and Line Q S are diameters of circle T. What is the measure of Arc S R? 50° 80° 100° 120°

Answer 1

Answer:

(C)100°

Step-by-step explanation:

See attached diagram to understand the problem better.

$|QT|=|PT| (radii of circle T)\\Therefore \triangle QPT is an isosceles triangle\\\angle PQT=\angle QPT=40^\circ (base angles of an isosceles triangle)$

$\angle PQT+\angle QPT+\angle PTQ=180^\circ (sum of angles in a \triangle )\\40^\circ+40^\circ+ \angle PTQ=180^\circ\\\angle PTQ=180^\circ-80^\circ\\\angle PTQ=100^\circ$

The measure of arc SR=Central Angle STR

$\angle PTQ=\angle STR (Vertically opposite angles)\\\angle STR=100^\circ\\mSR=100^\circ$