Vertically opposite angles?

Equal. They are opposite each other where two straight lines cross.

Exterior angle of a triangle?

Equals the sum of the two opposite interior angles.

What do you write after each step in an angle problem?

The reason, for example 'angles on a straight line add to 180^\circ'.

Angles, parallel lines and polygonsIB MYP Maths Extended: Flashcards

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Angles on a straight line?

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Angles on a straight line?: Add up to $180^\circ$ .
Angles around a point?: Add up to $360^\circ$ .
Vertically opposite angles?: Equal. They are opposite each other where two straight lines cross.
Angles in a triangle?: Add up to $180^\circ$ .
Exterior angle of a triangle?: Equals the sum of the two opposite interior angles.
Corresponding angles (parallel lines)?: Equal. F-shape.
Alternate angles (parallel lines)?: Equal. Z-shape.
Co-interior angles (parallel lines)?: Add up to $180^\circ$ . C-shape.
Sum of interior angles of an $n$ -sided polygon?: $(n-2)\times180^\circ$
Sum of the exterior angles of any polygon?: $360^\circ$
Exterior angle of a regular $n$ -gon?: $\frac{360^\circ}{n}$
Interior angle of a regular polygon from its exterior angle?: $180^\circ-\text{exterior angle}$
What do you write after each step in an angle problem?: The reason, for example 'angles on a straight line add to $180^\circ$ '.

Exam questions on Angles, parallel lines and polygons

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
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
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

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).