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Maths 3 marks

T1 CH4 Geometry · Tamil Nadu Board STD 6 (Tamil - English Medium). 10 questions.

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3 marks

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10 questions · timed · auto-graded

Question 13 Marks
Two supplementary angles are in ratio $5 : 4.$ Find the angles
Answer
Let the angles be $5 x$ and $4 x$ According to the problem
$ 5 x+4 x=180^{\circ}$
$9 x=180^{\circ}$
$x=\frac{180^{\circ}}{9}$
$x=20^{\circ} $
$\therefore$ Two angles are
(i) $5 x=5 \times 20^{\circ}=100^{\circ}$
(ii) $4 x=4 \times 20^{\circ}=80^{\circ}$
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Question 23 Marks
Given two angles are supplementary and one angle is $20^\circ$ more than other. Find the two angles
Answer
Let the angles be $x$ and $x+20^{\circ}$ According to the problem,
$ x+x+20^{\circ}=180^{\circ}$
$2 x+20^{\circ}=180^{\circ}$
$2 x=180^{\circ}-20^{\circ}$
$2 x=160^{\circ}$
$x=\frac{160^{\circ}}{2}$
$x=80^{\circ}$
$x+20^{\circ}=80^{\circ}+20^{\circ}$
$=100^{\circ} $
$\therefore$ The two angles are $80^{\circ}$ and $100^{\circ}$
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Question 33 Marks
Which angle is equal to two-third of its supplement?
Answer
Let the angle be $x$ According to the problem,
$ x=\frac{2}{3} \times\left(180^{\circ}-x\right)$
$3 x=2\left(180^{\circ}-x\right)$
$3 x=360^{\circ}-2 x$
$3 x+2 x=360^{\circ}$
$5 x=360^{\circ}$
$x=\frac{360^{\circ}}{5}$
$x=72^{\circ} $
$\therefore$ The angle is $72^{\circ}$
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Question 73 Marks
From the given figure, name the
(i) parallel lines
(ii) intersecting lines
(iii) points of intersection.
Answer
(i) $\overleftrightarrow{C D}$ and $\overleftrightarrow{E F}, \overleftrightarrow{C D}$ and $\overleftrightarrow{I J}, \overleftrightarrow{E F}$ and $\overleftrightarrow{I J}$
(ii) $\overleftrightarrow{A B}$ and $\overleftrightarrow{C D}, \overleftrightarrow{A B}$ and $\overleftrightarrow{E F}, \overleftrightarrow{A B}$ and $\overleftrightarrow{I J}, \overleftrightarrow{G H}$ and $\overleftrightarrow{I J}, \overleftrightarrow{A B}$ and $\overleftrightarrow{G H}$
(iii) $P, Q$ and $R$
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Question 83 Marks
Construct a line segment using ruler and compass.
AB = 7.5 cm
Answer

(i) Draw a line $l$ and mark a point $A$ on it.
(ii) Measure $7.5 cm$ using compass, placing the pointer at ' $O$ ' and the pencil pointer at $7.5 cm$
(iii) Place the pointer of the compass at A then draw a small arc on the line I with the pencil pointer.It cuts the line I at a point and names that point as B.
(iv) Now $\overline{ AB }$ is the required line segment of length $7.5 cm$
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Question 93 Marks
Construct a line segment using ruler and compass.
AB = 7.5 cm
Answer

(i) Draw a line $I$ and mark a point $C$ on it.
(ii) Measure $3.6 cm$ using compass, placing the pointer at $O$ and the pencil pointer at $3.6 cm$
(iii) Place the pointer of the compass at C then draw a small arc on the line I with the pencil pointer. It cuts the line I at a point and names the point as D.
(iv) Now $\overline{C D}$ is the required line segment of length $3.6 cm$
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Question 103 Marks
Construct a line segment using ruler and compass.
QR = 10 cm
Answer

(i) Draw a line I and mark a point Q on it.
(ii) Measure $10 cm$ using compass placing the pointer at $O$ and the pencil pointer at $10 cm$
(iii) Place the pointer of the compass at $Q$ then draw a small arc on the line I with the pencil pointer.It cuts the line I at a point and names that point as R.
(iv) Now $\overline{ QR }$ is the required line segment of length $10 cm$
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