Revision notes
Tell acute, right, obtuse, straight and reflex angles apart, and use complements, supplements and angles at a point.
At 3 o'clock the hands of the clock in Aisha's classroom make a perfect corner. At 6 o'clock they make a straight line. The amount of turn between the two hands is an angle, and every angle has a type.
An angle is the amount of turn between two lines that meet at a point, called the vertex.
We measure angles in degrees (°) with a protractor. A full turn is 360°, half a turn is 180° and a quarter turn is 90°.
🔑 Key idea: An angle measures turn. Full turn = 360°, half turn = 180°, quarter turn = 90°.
Acute: less than 90°. Right angle: exactly 90°, like the corner of your exercise book.
Obtuse: between 90° and 180°. Straight angle: exactly 180°, a straight line.
Reflex: between 180° and 360°, more than half a turn.
So 65° is acute, 120° is obtuse and 250° is reflex.
🔑 Key idea: Compare with 90° and 180° to decide the type.
Two angles are complementary if they add up to 90°. The complement of 35° is 90° − 35° = 55°.
Two angles are supplementary if they add up to 180°. The supplement of 35° is 180° − 35° = 145°.
Angles that meet at a point go all the way round, so they add up to 360°. On a clock, each hour gap is 360° ÷ 12 = 30°.
🔑 Key idea: Complementary → 90°, supplementary → 180°, angles at a point → 360°.
What type of angle is 77°?
Step 1: Compare with 90° and 180°
77° is less than 90°, so it is an acute angle.
Answer: Acute
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