Protractors commonly extend to 180°; though there are protractors that include the whole circle, that is, which extend to 360°.

199. Make of a piece of card as accurate a protractor as you can.

200. Make by a protractor an angle of 45°, and prove by geometry whether it is accurate

or not.

201..Can you contrive to divide a square into two equal but dissimilar parts?

202. Make with a protractor an angle of 60°, and prove by geometry whether it is cor

rect or not.

203. Make an angle, and determine by the protractor the number of degrees it contains.

204. Make by geometry the arc of a quad

rant, and determine by the protractor the number of degrees that are subtends.

205. Show how many hexagons may be made. to touch one hexagon at the sides.

That which an angle lacks of a right angle, that is, of 90°, is called its complement.

206. Make a few angles, and say which their complements are.

207. Make an angle of 70°, and measure its. complement.

That which an angle lacks of 180° is called its supplement.

208. Make a few angles, and their supplements, and measure them by the protractor.

209. Make by geometry an angle of 30°, and its supplement, and measure by the protractor the correctness of each.

210. Can you make a semicircle equal to a circle?

211. Make a few triangles of different forms, and measure by the protractor the angles of each, and see if you can find a triangle whose angles

added together amount to more than the angles of any other triangle added together.

212. Can you make a pentagon in a circle by means of the protractor?

213. Make of one picce of card a hollow square pyramid, and let the slant height be twice the diagonal of the base. Give a plan of your method, and a sketch of the pyramid, when completed.

214. Can you make a pentagon outside a circle by means of a protractor?

215. Can you, by means of a protractor, make a pentagon without using a circle at all?

It has already been said that the chord of an arc is a line joining the extremities of that arc.

216. With the assistance of a semicircular protractor, can you contrive to place on one line the chords of all the degrees from 1° to 90°? or, in other words, can you make a line of chords?

217. Can you say why the line of chords should not extend as far as 180°?

There is one chord which is equal in length to the radius of the quadrant to which all the chords belong; that is, which is equal to the radius of the line of chords.

218. Say which chord is equal to the radius of the line of chords.

219. Make, by the line of chords, angles of 26°, 32°, 75°, and prove, by the protractor, whether they are correct or not.

220. How, by the line of chords, will you make an obtuse angle, say one of 115°?

221. Can you make, with the assistance of a line of chords, a triangle whose angles at the base shall each be double of the angle at the vertex?

222. Make a triangle, whose sides shall be 21, 15, and 12, and measure its angles by the line of chords and by the protractor.

223. There is one side of a right-angled triangle that is longer than either of the other two. Give its name, and show from such fact that the chord of 45° is longer than half the chord of 90°.

224. Make by the protractor an angle of 90°, and give a figure to show which you consider the most convenient way of holding the protractor, whep, to a line, you wish to raise or let fall a perpendicular.

225. Can you make an isosceles triangle, having its base 1, and the sum of the other two sides 3?

226. Can you determine, by means of the scale, the length of the hypothenuse of a rightangled triangle, whose base is 4, and perpendicular 3?

227. Place a hexagon inside a circle, and another outside, in such positions with regard to each other as to show the ratio the inner one has to the outer.

By the area of a figure is meant its superficial contents, as expressed in the terms of any specified system of measures.

In England, the system of linear measures squared is generally 1 used to exprèss areas; as

1

'The terms acres and roods are the exceptions.