2 Mark Question

Question 12 Marks

A quadrilateral has three acute angles each measures 80°. What is the measure of fourth angle?

Answer

Sum of four angles of a quadrilateral = 360°
Sum of three angles having each angle equal to 80°
= 80° × 3 = 240°
Let fourth angle = x
Then,
240° + x = 360°
⇒ x° = 360° – 240°
⇒ x° = 120°
Fourth angle = 120°

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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° = 360°
⇒ x° = $\frac{360}{4}$
= 90°
Each angle will be = 90°

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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°
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°, what is the sum of the remaining two angles?

Answer

Sum of four angles of a quadrilateral = 360°
and sum of two angle out of these = 180°
Sum of other two angles will be = 360° - 180°
= 180°

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Question 62 Marks

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

Answer

We know that the sum of interior angels of a hexagon = 720° (180° × 4)
⇒ x + x - 5 + x - 5 + 2x – 5 + 2x - 5 + 2x + 20 = 720°
⇒ 9x - 20 + 20 = 720
⇒ 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°, 72°, 55° and x°. Find the value of x.

Answer

Sum of four angles of quadrilateral is 360°
110° + 12° + 55° + x° = 360°
⇒ 237° + x° = 360°
⇒ x° = 360° - 237°
⇒ 123°
x = 123°

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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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