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neurologyYou need to know

• An angle measures the amount of turn between two rays meeting at a vertex and is measured in degrees; a full turn is `360^\circ`.
• A right angle is `90^\circ`, a straight angle is `180^\circ`, and a full turn is `360^\circ`.
• Acute angles are greater than `0^\circ` and less than `90^\circ`; obtuse angles are greater than `90^\circ` and less than `180^\circ`; reflex angles are greater than `180^\circ` and less than `360^\circ`.
• Perpendicular lines meet at a right angle of `90^\circ`.
• Angles on a straight line sum to `180^\circ`.
• Angles around a point sum to `360^\circ`.
• Vertically opposite angles are equal when two straight lines cross.
• The interior angles of any triangle add up to `180^\circ`.
• An isosceles triangle has two equal sides and therefore its base angles are equal.
• On a `360^\circ` protractor, you can measure angles in either direction and read from the inner or outer scale, starting at `0^\circ` aligned with the baseline arm.
• A reflex angle and its corresponding minor angle at the same vertex add to `360^\circ`.
• Angle measures should be written with the degree symbol, `^\circ`; measured angles should be given to the nearest degree unless stated otherwise, while angles found by calculation should remain exact unless the question explicitly requires rounding.

• Measure an angle accurately with a `360^\circ` protractor by placing the centre exactly on the vertex, aligning the baseline with one arm, choosing the correct zero, reading the appropriate inner or outer scale, and recording the size to the nearest degree with the `^\circ` symbol.
• Draw a given acute, obtuse, or reflex angle using a `360^\circ` protractor by drawing a baseline ray, marking the required degree on the correct scale from `0^\circ`, and drawing the second arm through the mark, labelling the angle.
• Estimate an angle before measuring by classifying it as acute, right, obtuse, straight, or reflex and using visual benchmarks of `45^\circ`, `90^\circ`, `180^\circ`, `270^\circ`, and `360^\circ` to give a plausible value within `\pm 5^\circ`.
• Compare two angles without full measurement by referencing benchmarks, such as larger or smaller than `90^\circ` or `180^\circ`, and justify which is greater.
• Calculate a missing angle within a right angle by forming `\text{sum} = 90^\circ` and using addition or subtraction to find the unknown, stating units.
• Calculate a missing angle on a straight line by forming `\text{sum} = 180^\circ` and using addition or subtraction to find the unknown, stating units.
• Calculate a missing angle in a triangle by forming `a + b + c = 180^\circ` and, where appropriate, using the isosceles property to equate base angles, then solving.
• Use the vertically opposite angles rule to find unknowns when two straight lines cross, explicitly stating that the opposite angles are equal.
• Solve simple linear equations that arise in angle problems, for example, `3x + 20 + x = 180^\circ`, and interpret the solution as an angle size, checking it against the relevant angle-sum rule.