Angles in parallel lines and polygons GCSE lesson: find each angle and give the reason

Angles: practice

Give each angle as a number of degrees. Write your reasons on paper as you go. The stretch is optional.

Diagnostic question: choose and explain

1. Two parallel lines are crossed by a third line. Two angles sit between the parallel lines, on the same side of the third line. One is 65°. What is the other?
   1. 295°
   2. 65°
   3. 115°
   4. 25°

Practice questions

1. Three angles on a straight line are 40°, 75° and x. Find x.
2. Four angles meet at a point: 90°, 110°, 85° and y. Find y.
3. An isosceles triangle has an angle of 40° between its two equal sides. What size is each of its other two angles?
4. Two horizontal parallel lines are crossed by a line sloping up to the right. At each crossing there are four angles: top-left, top-right, bottom-left and bottom-right. Sketch it first and mark the four at each crossing. Then put each pair of angles in the group that names it.They sort 10 items into Vertically opposite (equal) and Corresponding (equal) and Alternate (equal) and Co-interior (add up to 180°) and On a straight line (add up to 180°).
5. Two angles sit between two parallel lines, on opposite sides of the line crossing them. One is 64°, so the other is 64° too. Which reason, written beside the working, earns the mark?
   1. Z angles
   2. Alternate angles are equal
   3. Corresponding angles are equal
   4. They look the same size
6. Two co-interior angles are 2x + 10 and x + 20 (in degrees). They add up to 180°. Solve the equation line by line to find x. Write the numbers without the ° sign.They solve 2x + 10 + x + 20 = 180 line by line, each line checked as they write it.
7. A regular decagon has 10 sides. Find the size of each interior angle.
8. A pentagon's interior angles are x, x, 2x, 2x and 120°. Find x.
9. Can a regular polygon have an exterior angle of 50°?
   1. No: exterior angles must be multiples of 10°
   2. Yes: it has 7 sides
   3. Yes: any angle less than 180° works
   4. No: 360 ÷ 50 = 7.2, and a polygon can't have 7.2 sides
10. Stretch: each interior angle of a regular polygon is 4 times its exterior angle. How many sides does it have?

Support: For the sorting question: for each pair, ask first whether both angles are at the same crossing. If not, ask whether they are between the parallel lines, then whether they are on the same side of the line crossing them.

Angles: exit

Find both angles and write a reason for each, as a full sentence.

1. Two parallel lines are crossed by a third line. Angle p and an angle of 72° are alternate angles. Angle q is on a straight line with angle p. Find p and q, and write a reason for each.

Exit check

Two angles found and a reason written for each show who can do both.

Students answer the exit question on their own: two angles, a reason for each.

Angles: find them, give the reasons

Find each angle or letter, and write a reason for every step as a full sentence (for example, "alternate angles are equal").