Lines PTQ and PUR are tangent to a circle, as shown below. If angle QTA = 41 degrees and angle RUA = 63 degrees then find angle QPR, in degrees.
arc(TA) = 2·angle(QTA) ---> arc(TA) = 2·41 = 82
arc(AU) = 2·angle(RUA) ---> arc(AU) = 2·63 = 126
arc(TAU) = arc(TA) + arc(AU = 82 + 126 = 208
arc(TU) = 360 - arcTAU) = 360 - 208 = 152
angle(QPR) = ½( arc(TAU) - arc(TU) ) = ½( 208 - 152 ) = ½(56) = 28