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Home / Geometry / Solutions of exercise 6.2| Class Nine – Ten(9-10)|Geometry

Solutions of exercise 6.2| Class Nine – Ten(9-10)|Geometry

1.Define interior and exterior of an angle.

The set of all points lying in the plane on the side C of AB and B side of AC is the interior region of the angle ∠BAC. The set of all points not lying in the interior region or on any arm of the angle is called exterior region of the angle.

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2. If D,B,E are the three points in the same straight line ,state the names of the angles formed in the adjoining figure.

The names of the angles formed in the adjoining figure are: ∠DBA and ∠ABE are right angles. ∠ABC is an obtuse angle. ∠EBC is an obtuse angle. ∠CBD is an acute angle. ∠DBE is a straight angle.

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3. Define an adjacent angle. Explain its exterior side with the help of a diagram.

Adjacent lines: The angles having a common side and a common vertex and a lying on opposite sides of their common side are called the adjacent angles.

Or, two angles are called adjacent angles, if, and only if, they have a common vertex and a common side lying between them.

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In the adjoining figure, ∠MON and ∠NOP are two adjacent angles. O is their common vertex and ON is their common side. OM and OP are two exterior arms of the two angles.

Note: Angles that are placed side-by-side are called adjacent angles.

4. Define the following and explain with diagram. Vertically opposite angles, straight angle, complementary angle, supplementary angle, right angle, perpendicular angle, acute angle and obtuse angle.

Answer: Vertically opposite angles: An angle produced by the two rays opposite to the two sides of an angle, is called the vertically opposite angle of the given angle.

Or, nonadjacent angles formed by two intersecting lines are called vertical angles. Two vertical angles are always congruent. ∠AOD and ∠BOC are pair of  vertical angles as are ∠AOC and ∠BOD.

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Straight angle: The angle produced at the common end point of two rays opposite to one another is called a straight angle.

Or, a straight angle is an angle whose measure is exactly 180.In fig. ∠AOB is a straight angle.

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The complementary angles: Two angles are called complementary angles if the sum of their measures is 900.If two angles are complementary, either angle is called the complement of the other. Since ∠AOC+∠BOC=900, hence ∠AOC and ∠BOC are complementary.

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The supplementary angles: Two angles are called supplementary angles if the sum of their measure is 180.If two angles are supplementary, either angle is called supplement of other. Since in figure ∠AOC+∠BOC=1800,hence ∠AOC and ∠BOC  are supplementary.

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Right angle and Perpendicular: If two adjacent angles standing on the same straight line are equal to one another, then each of the two angles is called a right angle. The two sides of the right angle are perpendicular to one another. In Fig ∠AOC=∠BOC=900=one right angle. CO is perpendicular on AB at the point O.

Note: A right angle is an angle whose measure is exactly 900.

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Acute angle: An acute angle is an angle whose measure is greater than 0, but less than 900.In Fig since ∠AOB is less than 900, hence ∠AOB is an acute angle.

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Obtuse angle: An obtuse angle is an angle whose measure is greater than 900, but less than 1800 .In above Fig. since ∠BOC is greater than 900, hence ∠BOC is an obtuse angle.

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