5 mistakes learners make with angles on lines and at a point, each one named and explained.
Angles on a straight line make 180, and angles round a point make 360.
An angle on a straight line is worked out as 360 minus the one you were given.
360 is the number attached most firmly to angles, and both rules are learned together.
Question. Angles on a straight line, one of them 117 degrees
A common answer. 360 - 117 = 243
The answer. 180 - 117 = 63
Why. A straight line is half a turn, so it is 180.
Draw the line. Half a turn cannot be bigger than a whole one, and 243 is more than half of 360.
An angle on a straight line, or a pair of co-interior angles, is worked out from 90.
The right angle is the most familiar angle fact and 90 is the number that comes first.
Question. Angles on a straight line, one of them 65 degrees
A common answer. 90 - 65 = 25
The answer. 180 - 65 = 115
Why. The two angles sit along a straight line, not inside a right angle.
Look at the picture. If the two angles together make a straight line, the total is 180.
An angle is given as twice the one in the question.
Two lines crossing make two pairs of angles, and doubling feels like accounting for both.
Question. x is vertically opposite 74 degrees
A common answer. 2 x 74 = 148
The answer. 74
Why. There are two angles of 74 degrees, but each of them is still 74.
How many of an angle there are never changes how big each one is.
The correct rule is used and the subtraction itself comes out wrong.
Subtracting from 180 across a column boundary is where most of these go astray.
Question. 180 - 117
A common answer. 73
The answer. 63
Why. 180 minus 117: 180 minus 100 is 80, minus another 17 is 63.
Break the subtraction into round numbers first. It removes the column carry entirely.
An angle vertically opposite 74 degrees is given as 106.
The neighbouring angle really is 106, and both facts come from the same crossing lines.
Question. x is vertically opposite 74 degrees
A common answer. 180 - 74 = 106
The answer. 74
Why. Vertically opposite angles are equal, with no calculation at all.
Vertically opposite means across the X. Those two are always equal.
WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.