Tag: angle and its measurement

Questions Related to angle and its measurement

In a $\Delta$PQR, if $\angle P - \angle Q = 42^{\circ}$ and $\angle Q - \angle R = 21^{\circ}$, find $\angle P, \angle Q$ and $\angle R$.

mathematics and statistics angle and its measurement directed angles

  1. $\angle P = 105^{\circ} \angle Q = 53^{\circ} \angle R = 32^{\circ}$

  2. $\angle P = 25^{\circ} \angle Q = 53^{\circ} \angle R = 32^{\circ}$

  3. $\angle P = 95^{\circ} \angle Q = 53^{\circ} \angle R = 32^{\circ}$

  4. $\angle P = 75^{\circ} \angle Q = 53^{\circ} \angle R = 32^{\circ}$

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Correct Option: C
Explanation:

Given,
$\angle P - \angle Q = 42$ (I)
$\angle Q - \angle R = 21$ (II)
Sum of angles = 180
$\angle P + \angle Q + \angle R = 180$ (III)
Add all the three equations:
$2 \angle P + \angle Q = 180 + 42 + 21$
$2 \angle P + \angle Q = 243$ (IV)

Add I and IV,
$2 \angle P + \angle P = 243 + 42$
$3 \angle P = 285$
$\angle P = 95^{\circ}$
From IV, $\angle Q = 243 - 2\times 95$
$\angle Q = 53^{\circ}$
From II,
$\angle R = 53 - 21 = 32^{\circ}$

An exterior angle of a triangle is less than either of its interior opposite angles.

mathematics and statistics angle and its measurement directed angles

  1. True

  2. False

  3. Ambiguous

  4. Data Insufficient

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Correct Option: B
Explanation:

Answer is option B (False)
In any triangle, if one of the sides is produced, then the exterior angle is greater than either of the interior and opposite angles.
Hence the above statement is false

When an arm of an angle is extended to double its length, then the measure of the angle:

mathematics and statistics angle and its measurement directed angles

  1. Doubles

  2. Triples

  3. Remains the same

  4. Becomes half

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Correct Option: C
Explanation:

Angle remains the same if we extend the arms.

So option $C$ is correct.

When an arm of an angle is extended then the measure of angle: 

mathematics and statistics angle and its measurement directed angles

  1. doubles

  2. triples

  3. remains the same

  4. none of these

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Correct Option: C
Explanation:

When an arm of an angle is extended then the measure of angle remains the same.

An angle which measures $\displaystyle 0^{\circ}$ is called

mathematics and statistics angle and its measurement directed angles

  1. Obtuse angle

  2. Straight angle

  3. Zero angle

  4. Right angle

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Correct Option: C
Explanation:

An angle which measures $ {0}^{o} $ is a zero angle.

Compare the areas of the right angled triangles ABC and DEF in which $\displaystyle \angle A=30^{\circ},\angle B=90^{\circ},AC=4cm,\angle D=60^{\circ},\angle E=90^{\circ}: : and: : DE=4cm $

mathematics and statistics angle and its measurement directed angles

  1. $\displaystyle Ar\left ( \Delta ABC \right )> Ar\left ( \Delta DEF \right )$

  2. $\displaystyle Ar\left ( \Delta ABC \right )< Ar\left ( \Delta DEF \right )$

  3. $\displaystyle Ar\left ( \Delta ABC \right )= Ar\left ( \Delta DEF \right )$

  4. Can't say

Show answer
Correct Option: B

If two triangles are congruent, then they are

mathematics and statistics angle and its measurement directed angles

  1. Symmetrical

  2. Identical

  3. Equilateral

  4. Isosceles

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Correct Option: A
Explanation:
Two triangles are congruent but they may not be equilateral or isosceles. (Hence option C and D are wrong)

For two objects to be symmetrical, they must be the same size and shape, with one object having a different orientation from the first.

Identical shapes are the shapes that have exact same shape, size, and position.

Congruent triangles are symmetrical but they may not be identical (as orientation can be different)

Hence option A is correct.

The opening between two lines is called:

mathematics and statistics angle and its measurement directed angles

  1. angle

  2. point

  3. line

  4. transversal

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Correct Option: A
Explanation:

An $angle$ is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the $angle$ and the rays as the sides, sometimes as the legs and sometimes the arms of the $angle.$

The angle at a point is

mathematics and statistics angle and its measurement directed angles

  1. $90^\circ$

  2. $180^\circ$

  3. $300^\circ$

  4. $360^\circ$

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Correct Option: D
Explanation:

An angle is measured with reference to a circle with its centre at the common endpoint of the rays. Hence, the sum of angles at a point is always 360 degrees.

So option D is the correct answer.

The sum of exterior angles of a triangle is

mathematics and statistics angle and its measurement directed angles

  1. $180^\circ$

  2. $270^\circ$

  3. $360^\circ$

  4. $540^\circ$

Show answer
Correct Option: C
Explanation:

The sum of exterior angle of a triangle is $ { 360 } $
the interior angle of a triangle add upto  $ { 180 } $, For any given corner exterior angle is $ { 180 } $ minus interior angle.
So sum of exterior angle is (180-a)+(180-b)+(180-c)=3*180-(a+b+c)=540-180=$360^0$