A kite or an arrowhead.
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Only the pair of angles opposite the line of symmetry are equal. The other two angles that are bisected by the line of symmetry are not equal. if these angles were equal then the shape would be a rhombus.
An irregular pentagon such as a child's silhouette of a house: a rectangle shape (open at the top) forming the body of the house, with a triangular roof on of the rectangle. The vertical line through the apex of the roof is the line of symmetry. The two walls, and the two roof lines are the two sets of equal sides. The two right angles at the base are the one set of matching angles.
Pentagon
A Kite
A kite.