Check the question whether you can see oo not

the pic is not clear 

if your qstn is sm as this 

AB is a diameter of a circle with centre O and AT is a tangent. If angle AOQ=58 find angle ATQ.  

answer is 

Angle ABQ=1/2 angle AOQ
=1/2*58
=29
Angle A =90(AT is a tangent)
angle BAT+angle ABT +angle ATQ=180(angle sum 
property of triangle.) 
90+29+angle ATQ= 180
angle ATQ=180-119
angle ATQ=61