Answer:
Measure of angle PSQ = 12.5 (degree).
Step-by-step explanation:
Given:
A quadrilateral PQRS.
Exterior angle at Q = 155 (degree)
To find measure of angle PSQ.
Let the [tex]m\angle\ PSQ[/tex] be [tex]x[/tex]
According to the question.
As [tex]m\angle \ Q =155[/tex]
Adjacent angle to [tex]Q[/tex] is [tex]= (180-155)=25[/tex] [Using linear pair].
Note:Property of a parallelogram:
Diagonally opposite angles of a quadrilateral are equal.
Measure of [tex]\angle S[/tex] is equal to the measure of [tex]\angle Q[/tex]. [They are diagonally opposite].
[tex]m\angle S=m\angle Q=25\deg[/tex]
[tex]m\angle S =m\angle PSQ + m\angle QSR[/tex]
And [tex]m\angle PSQ=m\angle QSR[/tex] [Diagonal are angle bisector at the vertex]
[tex]m\angle S=m\angle PSQ +m\angle PSQ[/tex]
[tex]m\angle S= 2*m\angle PSQ[/tex]
[tex]\frac{m\angle S}{2} =m\angle PSQ[/tex]
[tex]\frac{25}{2} =m\angle PSQ[/tex]
[tex]12.5=m\angle PSQ[/tex]
So measure of angle PSQ = 12.5 (degrees).
