Hey there!!
In order to find the angle , we will use transversal rule.
... angle MAT = 9x + 27
... Because of the vertically opposite angles
... Angle HAY + angle TAY = 180
... Because both angles form a straight angle ... hence they are supplementary angles.
... 9x + 27 + 7x - 23 = 180
Combine all the like terms
... 16x + 4 = 180
Subtract 4 on both sides
... 16x = 176
Divide by 16 on both sides
... x = 11
Now plug in this value for the angle MAT which is 9x + 27
... 9 ( 11 ) + 27
... 99 + 27
... 126
Hence, the angle MAT is 126°
Hope my answer helps!!