Mathematics · Quantitative Aptitude

Geometry of Triangles and Angles

758 Questions

Triangle and angle geometry covers angle sums, properties of equilateral shapes, and right triangles. These principles form the basis of advanced quantitative aptitude sections. Practicing spatial problems helps secure points in exams.

Triangle angle sumsPythagorean theoremProperties of equilateral trianglesComplementary and supplementary anglesRight triangle formulas

Geometry of Triangles and Angles Questions

Multiple choice maths acute and obtuse angles types of angle measurement of an angle angles in our surroundings

If one angle at a point is reflex angle, the other at that point may be :

  1. Acute angle

  2. Obtuse angle

  3. Straight angle

  4. Acute or obtuse angle
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Angle formed at a point is $\displaystyle { 360 }^{ o }$. 

When one of angle is reflex it range from $\displaystyle { 180 }^{ o }$ to $\displaystyle { 360 }^{ o }$. 
If angle is $\displaystyle { 200 }^{ o }$ then the other angle is $\displaystyle { 160 }^{ o }$, i.e obtuse angle. 
If one reflex angle is $\displaystyle { 300 }^{ o }$ then other angle is $\displaystyle { 60 }^{ o }$ i.e acute angle.

Multiple choice maths acute and obtuse angles types of angle measurement of an angle angles in our surroundings

Sum of two obtuse angle results in:

  1. Acute angle

  2. Right angle

  3. Obtuse angle

  4. Reflex angle
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Obtuse angle ranges from $\displaystyle { 90 }^{ o }$ to $\displaystyle { 180 }^{ o }$
So, sum of least obtuse angle is $\displaystyle { 91 }^{ o }+{ 91 }^{ o }={ 182 }^{ o }$ which is a reflex angle.
Sum of maximum obtuse angle is $\displaystyle { 179 }^{ o }+{ 179 }^{ o }={ 358 }^{ o }$ which is a reflex angle.

Acute angle is the angle which is greater than $\displaystyle { 0 }^{ o }$ and less than $\displaystyle { 90 }^{ o }$.

Obtuse angle is the angle which is greater than $\displaystyle { 90}^{ o }$ and less than $\displaystyle {180 }^{ o }$.
Right angle is the angle which is equal to $90^o$.
Reflex angle is the angle which is greater than $\displaystyle {180}^{ o }$ and less than $\displaystyle {360 }^{ o }$.

Multiple choice maths acute and obtuse angles types of angle measurement of an angle angles in our surroundings

Which of the following is a reflex angle?

  1. $\displaystyle { 180 }^{ o }$
  2. $\displaystyle { 360 }^{ o }$
  3. $\displaystyle { 204 }^{ o }$
  4. $\displaystyle { 135 }^{ o }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Reflex angle must be between $\displaystyle { 180 }^{ o }$ and $\displaystyle { 360 }^{ o }$. It can't be equal to $\displaystyle { 180 }^{ o }$ or $\displaystyle { 360 }^{ o }$ as these are straight and complete angle respectively.

Acute angle is the angle which is greater than $\displaystyle { 0 }^{ o }$ and less than $\displaystyle { 90 }^{ o }$.

Obtuse angle is the angle which is greater than $\displaystyle { 90}^{ o }$ and less than $\displaystyle {180 }^{ o }$.
Right angle is the angle which is equal to $90^o$.
Reflex angle is the angle which is greater than $\displaystyle {180}^{ o }$ and less than $\displaystyle {360 }^{ o }$.

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

If the angle of a triangle are in the ratio of $2:3:4$, find the there angles 

  1. $40^{o}, 60^{o}, 80^{o}$
  2. $20^{o}, 40^{o}, 60^{o}$
  3. $30^{o}, 60^{o}, 90^{o}$
  4. $90^{o}, 180^{o}, 360^{o}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the angles of the triangle be $2x,3x, 4x$. 

Then
$2x+3x+4x=180^o$ [ Since sum of the interior angles of a triangle be $180^o$]
or, $9x=180^o$
or, $x=20^o$.
Then the angles of the triangle be $40^o, 60^o, 80^o$.

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

Find the angles in each of the following.
The angle whose complement is one sixth of its supplement

  1. $72^{\circ}$
  2. $32^{\circ}$
  3. $62^{\circ}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the angle be $x^0$.


Supplement angle $=(180^0-x)$

Complement angle $=(90^0-x)$

According to the question,
$\dfrac{1}{6}\times (180^0-x)=(90^0-x)$

$(180^0-x)=6(90^0-x)$

$180^0-x=540^0-6x$

$5x=360^0$

$x=72^0$


Hence, this is the answer.

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

Find the angles in each of the following.
The angle which is four times its supplement

  1. $144^{\circ}$
  2. $44^{\circ}$
  3. $14^{\circ}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the angle be $x^0$.


According to the question,
Supplement angle $=(180^0-x)\times 4$

So,

$x=720^0-4x$

$5x=720^0$

$x=144^0$


Hence, this is the answer.

Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

Find the angles in each of the following.
The angles whose supplement is four times its complement

  1. $60^{\circ}$
  2. $30^{\circ}$
  3. $120^{\circ}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the angle be $x^0$.


Supplement angle $=(180^0-x)$

Complement angle $=(90^0-x)$

According to the question,
$180^0-x=4(90^0-x)$

$180^0-x=360^0-4x$

$3x=180^0$

$x=60^0$


Hence, this is the answer.