2 Mark Question

Question 12 Marks

Observe the image shown in the adjacent figure and answer the following questions.

What time does this clock show ?
What is the measure of the angle between its two hands ?
At which other times is the angle between the hands congruent with this angle ?

Answer

3 o’ clock.
90°.
9 o’ clock.

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Question 22 Marks

Observe the given angles and write the names of those having equal measures.

Answer

i. ∠ABC and ∠SPM
ii. ∠NIT and ∠SRI
iii. ∠PTQ and ∠RTS

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Question 32 Marks

Try to draw triangles with the following data. Can you draw these triangles. If not, look for the reason why you could not draw so.$\triangle PQR$ in which $l(QR) = 2cm, l(PQ) = 4cm, l(PR) = 2cm.$

Answer

$ \mathrm{I}(\mathrm{QR})+\mathrm{I}(\mathrm{PR})=2 \mathrm{~cm}+2 \mathrm{~cm}$
$=4 \mathrm{~cm}$
$=I(P Q) $
But in a triangle, the sum of the length of any two sides of a triangle is always greater than the length of the third side.
Hence, $\triangle P Q R$ cannot be drawn.

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Question 42 Marks

Try to draw triangles with the following data. Can you draw these triangles. If not, look for the reason why you could not draw so.$\triangle ABC$ in which $m\angle A = 85^\circ, m\angle B = 115^\circ, l(AB) = 5cm.$

Answer

$ \mathrm{m} \angle \mathrm{A}+\mathrm{m} \angle \mathrm{B}=85^{\circ}+115^{\circ}$
$=200^{\circ}>180^{\circ} $
But the sum of the measures of the angles of a triangle is $180^{\circ}$ Hence, $\triangle A B C$ cannot be drawn.

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Question 52 Marks

On the line below, the distance between any two adjoining points shown on it is equal. Hence, fill in the blanks.