Copyright © University of Cambridge. All rights reserved.
'Hexapentagon' printed from https://nrich.maths.org/
Each interior angle of a regular pentagon is $108$ degrees, whilst each interior angle of a regular hexagon is $120$ degrees. The non-regular pentagon in the centre of the diagram contains two angles which are interior angles of the regular hexagon, two angles which are interior angles of the regular pentagon and a fifth angle, the one marked $x$. So: $x+2\times120+2\times108= 5\times108=540$.
Hence $x=84$.