Worksheets · Foundation and Higher

Angles at points, lines and parallel lines

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 2 marks
(a) Three adjacent angles on one side of a straight line are $41^\circ$ , $76^\circ$ and $x^\circ.$ Work out x. (2)
Question 2Non-calculator · 4 marks
Two co-interior angles between parallel lines are $(3x+4)^\circ$ and $(5x+4)^\circ$ .
(a) Find x. (2)
(b) Find the smaller angle. (2)
Question 3Non-calculator · 4 marks
A straight line $EF$ crosses the lines $AB$ and $CD$ at $G$ and $H$ . At $G$ the angles on one side of $EF$ are $(5x - 20)^\circ$ and $(3x + 8)^\circ$ , and they lie on the straight line $AB$ . At $H$ , the angle corresponding to the $(3x + 8)^\circ$ angle is $(2x + 30)^\circ$ .
(a) Is $AB$ parallel to $CD$ ? You must show how you get your answer. (4)
1. AB is not parallel to CD
2. AB is parallel to CD

Answers and marks

(a) $63$ °

(a) $\frac{43}{2}$

(b) $68.5$ °

(a) No: $x = 24$ , so the corresponding angles are $80^\circ$ and $78^\circ$ , which are not equal.

P1 Forming the equation from angles on a straight line.
P1 Solving to $x = 24$ .
P1 Working out both corresponding angles, $80^\circ$ and $78^\circ$ .
C1 "Not parallel", because the corresponding angles ( $80^\circ$ and $78^\circ$ ) are not equal.

Angles at points, lines and parallel lines

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