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Mathematics

How many degrees are there in :

(i) two right angles

(ii) 16\dfrac{1}{6} right angle

(iii) 1121\dfrac{1}{2} right angles

(iv) a straight angle

(v) 25\dfrac{2}{5} straight angle

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Answer

(i) two right angles

One right angle = 90°

∴ Two right angles = 2 x 90° = 180°

Hence, the answer is 180°.

(ii) 16\dfrac{1}{6} right angle

Right angle = 90°

16\dfrac{1}{6} right angle = 16×90\dfrac{1}{6} \times 90^{\circ} = 15°

Hence, the answer is 15°.

(iii) 1121\dfrac{1}{2} right angles

Let's convert mixed to improper fraction:

112=321\dfrac{1}{2} = \dfrac{3}{2}

Right angle = 90°

32\dfrac{3}{2} right angles = 32×90\dfrac{3}{2} \times 90^{\circ}

= 31×45\dfrac{3}{1} \times 45^{\circ}

= 135°

Hence, the answer is 135°.

(iv) a straight angle

A straight angle is always 180°.

Hence, the answer is 180°.

(v) 25\dfrac{2}{5} straight angle

Straight angle = 180°

25\dfrac{2}{5} straight angle = 25×180\dfrac{2}{5} \times 180^{\circ}

= 21×36\dfrac{2}{1} \times 36^{\circ}

= 72°

Hence, the answer is 72°.

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