Given:
QT and RW are diameters in circle P.
To find:
The measure of arc QW.
Solution:
RW is a diameter.
The sum of the angles in the diameter is 180°.
m∠RPQ + m∠QPW = 180°
40° + m∠QPW = 180°
Subtract 40° from both sides.
40° + m∠QPW - 40° = 180° - 40°
m∠QPW = 140°
The measure of the central angle is congruent to the measure of the intercepted arc.
m∠QPW = m(QW)
m(QW) = 140°
Therefore m(QW) is 140°.