lesson
State the reason, not just the number
1 · Learn
Angles on a straight line total 180° and around a point total 360°. Vertically opposite angles are equal. When a transversal crosses parallel lines, corresponding and alternate angles provide further equalities.
Parallel-line angle rules require parallel lines; do not assume they apply just because a sketch looks similar. Mark the given information and name the relationship you use.
The supplied diagram shows triangle ABC with a line through C GIVEN parallel to AB. Label the base angles alpha and beta, and the angle inside the triangle at C gamma. Alternate angles put an equal alpha and an equal beta beside gamma on the line through C. Together alpha + gamma + beta make a straight angle, so the triangle's angles sum to 180°. This is a reason using parallel lines, not proof by measuring one picture.
2 · Worked example
If an angle is 68°, its adjacent straight-line partner is 112°. Its vertically opposite angle is 68°, a different relationship.
3 · Your turn
An angle is 47°. Find its adjacent straight-line partner and its vertically opposite angle.
Check your answer
133° and 47° respectively.
4 · Apply your learning
Annotate a supplied parallel-line diagram, giving a reason beside every derived angle.
Adult guidance and safety
Require a reasoned method and an independent check. Use accurate number lines, geometric drawings and data displays where the task needs them. These text models require varied practice and diagnostic assessment before curriculum approval.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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