Question

From the data given in the adjoining figure, find the measure of ∠PTS. Also, find the measure of the exterior angle PTN.

Answer 1

It is given that ∠SPT = 60° and ∠PST = 80°
Using the angle sum property of ∆PST,
m∠SPT + m∠PST + m∠PTS = 180°
⇒ 60° + 80° + m∠PTS = 180°
⇒ 140° + m∠PTS = 180°
⇒ m∠PTS = 180° – 140°
⇒ m∠PTS = 40°
Thus, the measure of ∠PTS = 40°
Using the exterior angle property,
m∠PTN = m∠SPT + m∠PST
= 60° + 80°
= 140°
Thus, the measure of exterior angle, ∠PTN = 140°