Coaching Centre
Angles and parallel lines
Review of angle facts and parallel lines: corresponding, alternate and co-interior angles, with multi-step problems and reasons.
Angle facts
With parallel lines, all eight angles are one of just two sizes, and those two sizes add to 180°.
$AB \parallel CD$. A transversal meets $AB$ at $P$ and $CD$ at $Q$. $\angle APQ = 3x^\circ$ and $\angle PQD = (x + 40)^\circ$ are alternate angles. Find $x$.
Alternate angles $3x^\circ$ and $(x + 40)^\circ$ on parallel lines. Find $x$.
$2x = 40$.
Co-interior angles on parallel lines are $4y^\circ$ and $y^\circ$. Find $y$.
$5y = 180$.
On parallel lines, one angle is $65^\circ$. Find the co-interior angle.
$180 - 65$.
Alternate angles are $72^\circ$ and $78^\circ$. The lines are:
They should be equal.
Corresponding angles on parallel lines are $(2a + 30)^\circ$ and $80^\circ$. Find $a$.
$2a = 50$.
Which is a valid reason?
Full fact plus the parallel lines.
On parallel lines, an angle is $40^\circ$. Find the obtuse angle at the same crossing.
$180 - 40$.
Vertically opposite angles are $(3m - 15)^\circ$ and $(m + 75)^\circ$. Find $m$.
$2m = 90$.
New numbers every time. Keep going until you get five in a row.