Angles, from basic rules to circle theorems
Help Itzi the spider climb the clock to rescue his family! Solve cunning angle puzzles to reveal a path through each level’s maze of tangled webs and reach the goal. It’s sure to make your head spin!
In this maths game you control a tiny robotic spider named Itzi, who lives with his family at the top of a strange old grandfather clock.
One dark night, the clock struck midnight with a mighty mechanical ‘Clang!’. So loud was the noise that the whole clock rattled and shook, sending Itzi and his family tumbling down through its rusty innards. Now Itzi must climb back up the clock, rescue his stranded family members, and return home!
On each level Itzi must find a safe path through an intricate maze of tangled webs, solving cunning angle puzzles as he goes. You’ll need brains and bravery to succeed, so get going – Itzi’s family are depending on you!
How To Play
To start a game, click ‘Play’ and then ‘OK’ to skip past the family portrait. (As you rescue family members, their images appear in the portrait – save everyone to complete the painting!)
On the ‘Select Level’ screen, click on any unlocked level to begin play (locked levels are indicated by a padlock symbol). The first time you play, only Stage 1: Level 1 is available.
In each level, your ultimate goal is to guide Itzi safely to the Warp Gate. You don’t control Itzi’s movement directly; instead, you rotate the giant cog and then Itzi ‘rolls’ according to gravity.
Dotted around each level are blue Glo-Flies. Itzi must collect all the blue Glo-Flies to activate the Warp Gate – only then can he enter it and travel to the next level.
On some levels you will find special gold Glo-Flies. You don’t have to collect them to activate the Gate, but they’re worth big bonus points if you do. Typically gold Glo-Flies are tucked away in hard-to-reach places, designed to challenge expert players. If you can’t reach one on your first play-through, that’s okay – just move on and come back later when you’ve honed your skills!
At certain points, Itzi’s path to the Gate will be blocked by a coloured line. To remove the line, you must click on the angle puzzle of the same colour and input its value:
- If the angle value is correct, the line disappears and Itzi can pass.
- If the angle value is incorrect, the line remains in place and Itzi loses energy.
Itzi’s energy is shown by a bar in the top-left of the screen – if it runs out, you fail the level. You also fail the level if you don’t reach the Gate before time runs out. But don’t worry: you can always try again!
Itzi also loses energy if he hits the cog rim or bumps into dangerous obstacles, such as Laser Walls and Spike Balls.
The game can be controlled entirely with the mouse, or by a combination of mouse and keyboard – to enjoy the game at its best, we recommend the latter.
To rotate the cog and roll Itzi around the level, press the left and right arrow keys (when in Window mode, you can also use the A and D keys). If you prefer, you can also rotate the cog by clicking on the arrow buttons to the right of the screen.
To input angle values, first click on the angle to make an input box appear. Now enter the angle’s value using either the keyboard or the on-screen keypad. For faster play, you can also click on the input box again to confirm entries or to close it.
Removed lines reappear after a few seconds, but can be removed again by clicking on the angle (you don’t need to solve the puzzle again).
Should you get stuck and want to start the level afresh, click on the ‘Restart‘ button in the bottom-left corner of the screen (next to the 'Pause' and 'Help' buttons).
In more complex levels there will be times when you want to record important info, such as the sum of certain angles or the values of unlabelled angles. Don’t reach for a pen and paper – use the Notes function!
It’s easy to use: first double-click on any empty area inside the cog to create an input box, then enter the value you want to record (like when solving angle puzzles). Hey presto, your value is now displayed on-screen! The Notes function can be really useful, so be sure to make good use of it.
If you need to erase a Note, simply point at it (the mouse pointer will change to an eraser icon) and click.
Stages & Levels
This game features six Stages, each of which focuses on a different area of angles-related mathematics:
- Stage 1: Basics
- Angles at a right angle
- Angles on a line
- Angles at a point
- Vertically opposite angles
- Stage 2: Parallel Lines
- Corresponding angles
- Alternate angles
- Interior angles
- Stage 3: Triangles
- Angles in a scalene triangle
- Angles in an isosceles triangle
- Angles in an equilateral triangle
- Exterior angles of a triangle
- Stage 4: Quadrilaterals
- Angles in a rectangle and square
- Angles in a quadrilateral (i.e. a quadrilateral with no special properties)
- Angles in a parallelogram and rhombus
- Angles in a kite
- Angles in a trapezoid
- Stage 5: Polygons
- Exterior angles of a polygon
- Interior angles of a polygon
- Stage 6: Angles In Circles
- Triangles in circles
- Radius and chord bisection rule
- Right angle in a semi-circle rule
- Cyclic quadrilateral rule
- Angle at the center is twice the angle at the circumference rule
- Angles in the same segment are equal rule
- Radius and tangent perpendicularity rule
- Alternate segment theorem rule
When the ‘Select Level’ screen appears after starting a new game, the highest Stage reached is displayed by default. To play earlier Stages, simply click the Stage number on the clock to the left of the screen. The first time you play only Stage 1 is available, with higher Stages unlocking once you reach a certain Total Score.
Each Stage consists of 20 standard levels. When you first play a Stage, only Level 1 is available; as you complete each level, the next in sequence unlocks automatically. One of your lost family members awaits rescue at the end of each Stage – complete Level 20 to save them!
In each Stage, as well as the standard levels there are four secret bonus levels, each containing a special challenge designed for gaming masters! To unlock the first bonus level you must achieve C Rank or better in all 20 standard levels; to unlock the second you must achieve B Rank or better; to unlock the third, achieve A Rank or better; and to unlock the fourth, achieve S Rank.
Note that the bonus levels are not available in Challenge mode.
Your score for each level is the sum of four values:
- Energy Score
- 3,000 points × % energy remaining
- Blue Glo-Flies Score
- 500 points × blue Glo-Flies collected
- Gold Glo-Flies Score
- 1,000 points × gold Glo-Flies collected
- Time Bonus
- 1 point × seconds remaining
Example 1: You complete a level with 75% energy remaining (3,000 × 0.75 = 2,250 points) and with 78 seconds left on the timer (78 points). You collected 3 blue Glo-Flies (3 × 500 = 1,500 points) and no gold Glo-Flies (0 points).
So your score for the level is: 2,250 + 1,500 + 0 + 78 = 3,828 points.
Example 2: You complete a level with 40% energy remaining (3,000 × 0.4 = 1,200 points) and with 143 seconds left on the timer (143 points). You collected 2 blue Glo-Flies (2 × 500 = 1,000 points) and 2 gold Glo-Flies (2 × 1,000 = 2,000 points).
So your score for the level is: 1,200 + 1,000 + 2,000 + 142 = 4,343 points.
Your best score for each level is recorded automatically. The scores for all levels completed in a Stage are added together to create the Stage Score, and the scores for all unlocked Stages are added together to create the Total Score.
On completing a level you are awarded a Rank of either C (OK), B (Good), A (Great) or S (Amazing!). These are defined as:
- C Rank
- Complete the level with score equivalent to less than 66% energy remaining and no time bonus.
- B Rank
- Complete the level with score equivalent to more than 66% energy remaining and no time bonus.
- A Rank
- Complete the level with score equivalent to 100% energy remaining, all gold Glo-Flies collected and no time bonus.
- S Rank
- Complete the level with score equivalent to 100% energy remaining, all gold Glo-Flies collected and a fast time bonus. S Ranks can be tough to get – look for shortcuts and tricks that will help you save seconds!
Improve your score
- When you start a new level, spend a few moments to spot its main mathematical features. Are there any triangles that will be useful? Any parallel lines? Any circles that will help you with your calculations?
- Try to decide the best order in which to calculate the angles. Often you need to work out other angles in order to calculate the angles needed to remove lines.
- Make good use of the Notes function. The more correct angle values you add, the easier it will be to work out the angles you need.
- Sometimes it helps to imagine extra lines in your diagram to solve problems.
- You will need to remove some lines more than once. Remember that once you’ve correctly found an angle you can remove its line as often as you wish.
- Sometimes it’s useful to rest Itzi against a line you can remove; then, when you remove it, Itzi will start rolling. Use this control to your advantage when timing is important.
- As you progress through the game, you will need to use more and more facts about angles. Use the in-game math help to find out what you need to progress.
- Don’t assume that two lines are parallel or the same length unless they are marked as being so. It’s easy to think that because two lines look roughly the same length they are the same length. Likewise, it’s easy to think that two lines are parallel because they have roughly the same direction.
- It’s always possible to complete a level without Itzi taking any damage – and it’s the only way to get A and S Ranks!
- Getting an S Rank is tough... really tough! To earn them, you need to achieve or surpass the best scores of Mangahigh’s team of designers and testers. Not only do you need to be razor sharp on your math, get ALL the flies and take NO damage, you also need to complete the level in a super-fast time. Look for shortcuts and tricks that will save you seconds, and be prepared to take risks!
- If you can’t work out how to find an angle, use the in-game math help.
- Angles making a straight line add up to 180°.
- Angles meeting at a point add up to 360°.
- The angles in a triangle add up to 180°.
- In an isosceles triangle, two of the angles are equal. If you know one of the two equal angles, double it and then take the number you get away from 180° to find the other angle. If you know the angle which isn’t one of the two equal angles, take that away from 180° and then half your answer to find the other two (equal) angles.
- Look out for parallel lines. You can use corresponding angles and alternate angles with these.
- The exterior angles of a polygon add up to 360°. If you know that your polygon has equal sides then all its exterior angles will be the same, so divide 360° by the number of sides to work out the size of the exterior angle.
- The interior angles in a quadrilateral add up to 360°.
- Look out for circles and know the facts about angles in circles. Refer to the in-game math help if you are unsure.
- If you see a triangle in which two of the sides are radii of a circle then it is an isosceles triangle, as those two sides will be equal.