It is given in the question that,
Line QS bisects angle PQR. Solve for x and find the measure of angle PQR.
And 

Since QS bisects angle PQR, therefore

Substituting the values, we will get

 
        
                    
             
        
        
        
Answer:

Step-by-step explanation:
Given:
 °
°
From the triangle, using the theorem that center angle by an arc is twice the angle it subtend at the circumference.

Also, the diameter of the circle is BD. As per the theorem that says that angle subtended by the diameter at the circumference is always 90°, 

From the Δ BCD, which is a right angled triangle,

Now, using the theorem that angle between the tangent and a chord is equal to the angle subtended by the same chord at the circumference.
Here, chords CD and BC subtend angles 40 and 50 at the circumference as shown in the diagram by angles  and EF is a tangent to the circle at point C.
 and EF is a tangent to the circle at point C.
Therefore, 
Again, using the same theorem as above,

Hence, all the angles are as follows:
