Angles in the 11+ — Questions, Worked Answers and Practice Papers

A reflex angle is an angle that is greater than 180°. When two lines meet at a point (called a vertex) one side of the segment is less than 180° and the other side is more than 180°. The side which is more than 180° is the one with the reflex angle. {"object":"clock","size":200,"hour":10,"min":30,"hourColor":"red","minColor":"green"} {"shape":"arrow","size":80,"angle":-90,"labelTop":"This side is the reflex angle","color":"darkblue"} There are two ways to solve this problem, {"text":"bold","word":"Solution 1 - the faster way"} From 10 to 4, you can draw a straight line. The angle of a straight line is a flat angle, in other words, 180° A quarter in a clock is 90°. (If one hand is pointing at 12 and the other pointing at 3 then it will be a quarter with 90°.) There are 3 numbers in a quarter so every number will form, = 90 / 3 = 30° In other words, if one hand is at 12 and the other hand at 1 then it will be 30°. For every number jump, you can add another 30°. So if the hand is at 4 and it moves to 5 then it is 30° move and if it moves to 6 then it is a 60° move.  At 22:30, the hour hand is halfway between 10 and 11. When the hand moves from 10 to 4 it is a 180° move and from 4 to 6 is an additional 60° move. So the total move is,  180 + 60 = 240° but we need to subtract 15° because the hour hand is not pointing at 10, it is halfway between 10 and 11 at 22:30. 240° - 15° = 225° {"text":"bold","word":"Solution 2 - the better way"} There are 360° in a full circle in a clock and there are 12 numbers. Let's find out how many degrees is each number. We can do that by simply dividing 360° equally into 12 parts, = 360° / 12 = 30° So what this means is that when a needle moves from one number to the next it moves 30°. When it moves 2 numbers then it has moved 30° and 30°, or 2 x 30° = 60° So when we need to find the angle on the right side of 10 and 6, then we simply need to count how many numbers the needle needs to move from 10 to reach 6. If you counted 8 times then that is perfectly right.  As each number move is 30°, we can simply multiply this 8 times = 30° x 8 = 240°  but we need to subtract 15° because the hour hand is not pointing at 10, it is halfway between 10 and 11 at 22:30. 240° - 15° = 225° {"object":"video","url":"https://youtu.be/xzAGoErwAxg"}