BECE JHS
Angles on a straight line add to 180 degrees. Angles in a triangle add to 180 degrees. Parallel lines make equal angles in matching positions.
A right angle is 90 degrees. Angles that meet on a straight line add to 180 degrees. Angles around a point add to 360 degrees. Vertically opposite angles, the pair made when two lines cross, are equal. In any triangle the three interior angles add to 180 degrees. An equilateral triangle has three equal angles of 60 degrees. An isosceles triangle has two equal sides and the angles opposite those sides are equal.
When a straight line crosses a pair of parallel lines, corresponding angles are equal. They sit in the same position at each crossing. Alternate angles are equal. Interior angles on the same side of the crossing line add to 180 degrees. Name the reason beside the size. "70 degrees, corresponding angles" earns both the number and the reason. A bare number earns only the number.
A reason is a mark of its own on most written angle questions. Accept the standard names: corresponding angles, alternate angles, angles on a straight line, angles in a triangle. A diagram is not to scale unless the question says it is, so do not measure with a protractor unless you are told to. Show the sum you used, for example 180 − 115.
These are practice questions in the style of the paper, with a model answer and a mark scheme. They are not a promise of what your paper will ask.
2 marks
In triangle ABC, angle A is 40 degrees and angle B is 65 degrees. Find angle C, and give the reason. (2 marks)
Angle C = 180 − (40 + 65) = 180 − 105 = 75 degrees. The three angles of a triangle add to 180 degrees.
3 marks
Two parallel lines are crossed by a straight line. One of the angles formed is 70 degrees.
(a) State the size of the corresponding angle. (1 mark)
(b) Find the interior angle on the same side of the crossing line, and give the reason. (2 marks)
(a) 70 degrees.
(b) 110 degrees, because interior angles on the same side of the crossing line add to 180 degrees.
4 marks
Two straight lines cross. One angle is 128 degrees. Find the vertically opposite angle and one adjacent angle on the straight line. Give a reason for each. (4 marks)
The vertically opposite angle is 128 degrees, because vertically opposite angles are equal. An adjacent angle on the straight line is 180 − 128 = 52 degrees, because angles on a straight line add to 180 degrees.
More questions on this topic are inside GLearn, marked as you answer, with the reason written out. The first ones need no account.
Practise Mathematics free180 degrees. If you know two angles, subtract their sum from 180 to find the third. Write the reason "angles in a triangle" beside the answer.
Corresponding angles are equal, and alternate angles are equal. The interior angles on the same side of the crossing line are not equal. They add to 180 degrees. All BECE Mathematics past questions