2 Marks Questions

Question 12 Marks

A quadrilateral has three acute angles each measures $80^\circ .$ What is the measure of fourth angle$?$

Answer

Sum of four angles of a quadrilateral $= 360^\circ $
Sum of three angles having each angle equal to $80^\circ = 80^\circ \times 3 = 240^\circ $
Let fourth angle $= x$ Then, $240^\circ + x = 360^\circ $
$\Rightarrow x^\circ = 360^\circ – 240^\circ $
$ \Rightarrow x^\circ = 120^\circ $
Fourth angle $= 120^\circ $

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Question 22 Marks

Define the following terms: Convex Quadrilateral.

Answer

Convex Quadrilateral: A quadrilateral is called a convex quadrilateral of the line containing any side of the quadrilateral has the remaining vertices on the same side of it. In the figure quadrilateral $ABCD$ is a convex quadrilateral.

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Question 32 Marks

A quadrilateral has all its four angles of the same measure. What is the measure of each$?$

Answer

Let each equal angle of a quadrilateral $= x$
$4x^\circ = 360^\circ $
$\Rightarrow x^\circ =\frac{360}{4} = 90^\circ $
Each angle will be $= 90^\circ $

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Question 42 Marks

Find the number of degrees in each exterior angle of a regular pentagon.

Answer

In a pentagon or a polygon, sum of exterior angles formed by producing the sides in order, is four right angles or $360^\circ $ Each exterior angle $=\frac{360}{5}=72^\circ$

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Question 52 Marks

If the sum of the two angles of a quadrilateral is $180^\circ ,$ what is the sum of the remaining two angles$?$

Answer

Sum of four angles of a quadrilateral $= 360^\circ $ and
sum of two angle out of these $= 180^\circ $
Sum of other two angles will be $= 360^\circ - 180^\circ = 180^\circ $

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Question 62 Marks

The measure of angles of a hexagon are $x^\circ , (x - 5)^\circ (x - 5)^\circ , (2x - 5)^\circ , (2x - 5)^\circ , (2x + 20)^\circ .$ Find the value of $x.$

Answer

We know that the sum of interior angels of a hexagon $= 720^\circ (180^\circ \times 4)$
$\Rightarrow x + x - 5 + x - 5 + 2x – 5 + 2x - 5 + 2x + 20 = 720^\circ $
$\Rightarrow 9x - 20 + 20 = 720$
$\Rightarrow 9x = 720$
$\Rightarrow\text{x}=\frac{720}{9}=80^\circ$
$\text{x}=80^\circ$

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Question 72 Marks

The angles of a quadrilateral are $110^\circ , 72^\circ , 55^\circ $ and $x^\circ .$ Find the value of $x.$

Answer

Sum of four angles of quadrilateral is $360^\circ $
$110^\circ + 12^\circ + 55^\circ + x^\circ = 360^\circ $
$\Rightarrow 237^\circ + x^\circ = 360^\circ $
$\Rightarrow x^\circ = 360^\circ - 237^\circ $
$\Rightarrow 123^\circ$
$x = 123^\circ $

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Question 82 Marks

Define the following terms: Quadrilateral

Answer

Quadrilateral: A closed figure made of four line segment is called a quadrilateral such that,

No three points of them are collinear.
The line segments do not intersect except at their ends points.

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