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Step-by-step build — 4 steps. Also available as a print sheet.
Set the miter saw to a 30° bevel and cut five 1x2s, with ends parallel, to 13" overall length (long point to short point). Then set the miter saw to a 24° bevel and cut each 13" piece into two smaller pieces as shown in the diagram, giving 10 point segments total.
Glue one shorter and one longer segment together to form each of the five star points. Hot glue works well, but regular wood glue is fine too — just let it dry. Nailing the joints adds extra strength, though nailing at this angle is a little tricky.
Nail and glue the five point sections together to form the complete star.
Place the assembled star on the plywood backer and trace the outline. Cut out the shape with a jigsaw. Glue and nail the backer to the back of the star with shorter nails.