Answer :

AL2006

Angle-5 and angle-7 are 'vertical angles', so they're equal,
and we can write ...
                                           10x- 9  =  9x

Subtract  9x  from each side:  x - 9 = 0

Add  9  to each side:               x     =  9

Now that we know what 'x' is, we can find the size of Angles-5  and -7 .

Angle-7  =  9x  = 81° .

Now look at Angle-6 ... the one that's the answer to the problem.

Angle-6  and -7 together make a straight line, so they must
add up to 180°.

                                     Angle-6  +  81°  =  180°

Subtract 81° from each side:    Angle-6  =  99° .