Mathematics · Quantitative Aptitude

Geometry of Triangles and Angles

846 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 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.

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 two times its complement

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

  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,
Complement angle $=(90^0-x)\times 2$

So,

$x=180^0-2x$

$3x=180^0$

$x=60^0$


Hence, this is the answer.