Angles, parallel lines and polygonsIB MYP Maths Standard: Subtopic test

1. 1
   Straight lines $AB$ and $CD$ cross at the point $O$. Angle $AOC=(3x+10)^\circ$ and angle $COB=(2x+20)^\circ$.

   (a)

   Find the value of $x$.

   [1 mark]

   • A$10$
   • B$30$
   • C$34$
   • D$36$

   (b)

   Find the size of angle $AOD$.

   [1 mark]

   • A$80^\circ$
   • B$100^\circ$
   • C$30^\circ$
   • D$280^\circ$

   (c)

   Ray $OE$ bisects angle $AOC$. Find angle $EOB$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Line $PQ$ is parallel to line $RS$. A straight line crosses $PQ$ at $X$ and $RS$ at $Y$, and is extended beyond $Y$ to a point $Z$. Points $P$ and $R$ are on the same side of the crossing line, and $X$ is above $Y$. Angle $PXY=64^\circ$.

   (a)

   Find the size of angle $XYR$.

   [1 mark]

   • A$64^\circ$
   • B$26^\circ$
   • C$116^\circ$
   • D$296^\circ$

   (b)

   Angle $PXY=64^\circ$. Which reason gives $QXY=116^\circ$ directly from $PXY$, without using the parallel lines?

   [1 mark]

   • AAlternate angles are equal
   • BCorresponding angles are equal
   • CVertically opposite angles are equal
   • DAngles on a straight line add up to $180^\circ$

   (c)

   Find the size of angle $RYZ$ and give a reason for your answer.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In triangle $ABC$, side $BC$ is extended to a point $D$. Angle $BAC=x^\circ$, angle $ABC=(2x+5)^\circ$ and the exterior angle $ACD=(5x-15)^\circ$.

   (a)

   Write an equation in $x$ using the exterior angle property of a triangle, and hence find $x$.

   [3 marks]

   (b)

   Find angle $ACB$. Hence classify triangle $ABC$ as acute-angled, right-angled or obtuse-angled, justifying your answer.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A tile designer is working with regular polygons. Polygon $P$ has an exterior angle of $15^\circ$. Polygon $Q$ has $12$ sides.

   (a)

   (i) Find the number of sides of $P$.
   (ii) Find the size of each interior angle of $P$.
   (iii) Find the sum of the interior angles of $P$.

   [6 marks]

   (b)

   Polygon $Q$ is regular.
   (i) Find the size of each interior angle of $Q$.
   (ii) Show that one regular $12$-sided polygon, one regular hexagon and one square fit together exactly around a point.
   (iii) Polygon $P$ and polygon $Q$ and a square are placed together around a point. Explain whether they fit exactly.

   [6 marks]

   Total for question 4: 12 marks

End of questions