Angles, parallel lines and polygonsIB MYP Maths Standard: Mind map

Exam questions on Angles, parallel lines and polygons

1. Straight lines $AB$ and $CD$ cross at the point $O$. Angle $AOC=(3x+10)^\circ$ and angle $COB=(2x+20)^\circ$.
   Ray $OE$ bisects angle $AOC$. Find angle $EOB$.2 marks
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 $PXY=64^\circ$.
   Find the size of angle $RYZ$ and give a reason for your answer.2 marks
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 $ACD=(5x-15)^\circ$.
   Write an equation in $x$ using the exterior angle property of a triangle, and hence find $x$.3 marks