Angles and triangles.

Step 1 of 6

Angles on a straight line

An angle measures how far you turn to get from one direction to another. A full turn is $360^\circ$⁠, so a straight line, half a turn, is $180^\circ$⁠, and the corner of a page, a quarter turn, is $90^\circ$⁠.

When a ray leaves a point on a straight line, it splits the half turn into two angles side by side. Work out how many degrees the second angle has, then choose Worked out under Look inside to check.

Step 2 of 6

Vertically opposite angles

Carry the ray on past the point and you get two straight lines crossing, with four angles around the crossing point. Any two neighbouring angles sit together on one of the lines, so they add up to $180^\circ$⁠. Predict how big the angle opposite the given one is.

Step 3 of 6

Parallel lines

Two parallel lines never meet: they run in the same direction. A third line that cuts both of them, a transversal, leans to them at the same angle at both crossings. So angles in the same position at the two crossings are equal; they are called corresponding angles.

Two more rules follow. Alternate angles, between the two lines and on opposite sides of the transversal, are equal. Co-interior angles, between the lines and on the same side of the transversal, add up to $180^\circ$⁠. Answer, then choose Worked out under Look inside.

Step 4 of 6

The angles of a triangle

Now the board holds a triangle. Angle A and Angle B are the angles at the two ends of the base $AB$⁠, and the third angle, at $C$⁠, follows by itself. Predict what happens when the three corners are torn off and laid side by side.

Step 5 of 6

A right triangle

What you saw holds in every triangle: $A + B + C = 180^\circ$$A + B + C =$$180^\circ$⁠. So once two angles are known, the third is fixed. Here Angle A is locked and the angle at $C$⁠ is hidden: work it out first, and only then move Angle B.

Step 6 of 6

The exterior angle

Carry the base $AB$⁠ on past $B$⁠. Between the extension and the side $BC$⁠ there is now an angle outside the triangle: an exterior angle. It sits on a straight line with the angle $B$⁠, so the two add up to $180^\circ$⁠. Once you have answered, choose Worked out under Look inside and see where the corners at $A$⁠ and $C$⁠ go.