<?xml version="1.0" encoding="utf-8"?>
<!-- More Geometry Snacks #3 (Curiosity Closet), drawn by hand as a ruler-and-compass construction.
     The figure is rigid (see below), and a handle could only turn it, so nothing is dragged: the center O and the
     big pentagon's top vertex Tp are the hidden base points, and the circumcircle is the circle about O through Tp. The big
     pentagon is the classic compass construction on O and Tp: W on the perpendicular diameter, M its midpoint, the
     circle about M through Tp cutting the diameter at N, and TpN is the side, stepped round the circumcircle to R and
     BR; L and BL are their reflections in the axis OTp. The dashed diagonal is BL Tp. The small pentagon is the
     dilation of the big one about O whose upper-left vertex UL is on that diagonal: UL is where the line OL meets the
     diagonal (which fixes the small pentagon: UL is the midpoint of the diagonal and the ratio is cos 72 degrees, so
     the statement leaves nothing free but the figure's size and turn), and the rest by parallels to the big sides
     through UL and reflections in the axis. The blue segments run from BL to the small pentagon's bottom-right vertex
     BR2 and on to its top vertex T2; the asked angle is at BR2 between them. -->
<Drawing Version="1">
  <Viewport Left="-4.7" Top="4.7" Right="4.7" Bottom="-4.7" />
  <Scene Left="-4.7" Top="4.7" Right="4.7" Bottom="-4.7" />
  <Styles>
    <PointStyle Name="Dot" Size="8" Fill="#FF404040" Color="#FF404040" StrokeWidth="1">
      <Dark Fill="#FFE8EBF0" Color="#FFE8EBF0" />
    </PointStyle>
    <ShapeStyle Name="Blue" Color="#FF0000FF" StrokeWidth="3" Fill="#FFB9B9FF">
      <Dark Color="#FF9DA3FF" Fill="#FF7F86D6" />
    </ShapeStyle>
    <LineStyle Name="BlueLine" Color="#FF0000FF" StrokeWidth="3">
      <Dark Color="#FF9DA3FF" />
    </LineStyle>
    <LineStyle Name="Dashed" Color="#FF000000" StrokeWidth="2.5" Dash="Dash">
      <Dark Color="#FFE8EBF0" />
    </LineStyle>
    <ShapeStyle Name="Frame" Color="#FF000000" StrokeWidth="3" IsFilled="false">
      <Dark Color="#FFE8EBF0" />
    </ShapeStyle>
  </Styles>
  <Figures>
    <FreePoint Name="O" Style="Dot" Locked="true" X="0" Y="0" />
    <FreePoint Name="Tp" Visible="false" Locked="true" X="0" Y="4" />
    <Circle Name="circumcircle" Visible="false">
      <Dependency Name="O" />
      <Dependency Name="Tp" />
    </Circle>
    <Segment Name="OTp" Visible="false">
      <Dependency Name="O" />
      <Dependency Name="Tp" />
    </Segment>
    <LineTwoPoints Name="axis" Visible="false">
      <Dependency Name="O" />
      <Dependency Name="Tp" />
    </LineTwoPoints>
    <PerpendicularLine Name="diameter" Visible="false">
      <Dependency Name="OTp" />
      <Dependency Name="O" />
    </PerpendicularLine>
    <IntersectionPoint Name="W" Visible="false" Algorithm="IntersectLineAndEllipse2">
      <Dependency Name="diameter" />
      <Dependency Name="circumcircle" />
    </IntersectionPoint>
    <MidPoint Name="M" Visible="false">
      <Dependency Name="O" />
      <Dependency Name="W" />
    </MidPoint>
    <Circle Name="aboutM" Visible="false">
      <Dependency Name="M" />
      <Dependency Name="Tp" />
    </Circle>
    <IntersectionPoint Name="N" Visible="false" Algorithm="IntersectLineAndEllipse1">
      <Dependency Name="diameter" />
      <Dependency Name="aboutM" />
    </IntersectionPoint>
    <CircleByRadius Name="sideFromTp" Visible="false">
      <Dependency Name="Tp" />
      <Dependency Name="N" />
      <Dependency Name="Tp" />
    </CircleByRadius>
    <IntersectionPoint Name="R" Visible="false" Algorithm="IntersectCircleAndCircle1">
      <Dependency Name="circumcircle" />
      <Dependency Name="sideFromTp" />
    </IntersectionPoint>
    <CircleByRadius Name="sideFromR" Visible="false">
      <Dependency Name="Tp" />
      <Dependency Name="N" />
      <Dependency Name="R" />
    </CircleByRadius>
    <IntersectionPoint Name="BR" Visible="false" Algorithm="IntersectCircleAndCircle1">
      <Dependency Name="circumcircle" />
      <Dependency Name="sideFromR" />
    </IntersectionPoint>
    <ReflectedPoint Name="L" Visible="false">
      <Dependency Name="R" />
      <Dependency Name="axis" />
    </ReflectedPoint>
    <ReflectedPoint Name="BL" Visible="false">
      <Dependency Name="BR" />
      <Dependency Name="axis" />
    </ReflectedPoint>
    <Polygon Name="big" Style="Frame">
      <Dependency Name="Tp" />
      <Dependency Name="R" />
      <Dependency Name="BR" />
      <Dependency Name="BL" />
      <Dependency Name="L" />
    </Polygon>
    <Segment Name="diagonal" Style="Dashed">
      <Dependency Name="BL" />
      <Dependency Name="Tp" />
    </Segment>
    <LineTwoPoints Name="OL" Visible="false">
      <Dependency Name="O" />
      <Dependency Name="L" />
    </LineTwoPoints>
    <IntersectionPoint Name="UL" Visible="false" Algorithm="IntersectLineAndLine">
      <Dependency Name="OL" />
      <Dependency Name="diagonal" />
    </IntersectionPoint>
    <LineTwoPoints Name="LTp" Visible="false">
      <Dependency Name="L" />
      <Dependency Name="Tp" />
    </LineTwoPoints>
    <ParallelLine Name="topSide" Visible="false">
      <Dependency Name="LTp" />
      <Dependency Name="UL" />
    </ParallelLine>
    <IntersectionPoint Name="T2" Visible="false" Algorithm="IntersectLineAndLine">
      <Dependency Name="topSide" />
      <Dependency Name="axis" />
    </IntersectionPoint>
    <LineTwoPoints Name="LBL" Visible="false">
      <Dependency Name="L" />
      <Dependency Name="BL" />
    </LineTwoPoints>
    <ParallelLine Name="leftSide" Visible="false">
      <Dependency Name="LBL" />
      <Dependency Name="UL" />
    </ParallelLine>
    <LineTwoPoints Name="OBL" Visible="false">
      <Dependency Name="O" />
      <Dependency Name="BL" />
    </LineTwoPoints>
    <IntersectionPoint Name="BL2" Visible="false" Algorithm="IntersectLineAndLine">
      <Dependency Name="leftSide" />
      <Dependency Name="OBL" />
    </IntersectionPoint>
    <ReflectedPoint Name="R2" Visible="false">
      <Dependency Name="UL" />
      <Dependency Name="axis" />
    </ReflectedPoint>
    <ReflectedPoint Name="BR2" Visible="false">
      <Dependency Name="BL2" />
      <Dependency Name="axis" />
    </ReflectedPoint>
    <Polygon Name="small" Style="Frame">
      <Dependency Name="T2" />
      <Dependency Name="R2" />
      <Dependency Name="BR2" />
      <Dependency Name="BL2" />
      <Dependency Name="UL" />
    </Polygon>
    <Segment Name="toCorner" Style="BlueLine">
      <Dependency Name="BL" />
      <Dependency Name="BR2" />
    </Segment>
    <Segment Name="toTop" Style="BlueLine">
      <Dependency Name="BR2" />
      <Dependency Name="T2" />
    </Segment>
    <AngleArc Name="asked" Style="Blue" Radius="40">
      <Dependency Name="BR2" />
      <Dependency Name="BL" />
      <Dependency Name="T2" />
    </AngleArc>
  </Figures>
</Drawing>
