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

The difference between two angles is $19$$\displaystyle ^{o}$ and their sum is $\displaystyle \frac{890}{9}^o$. Find the greater angle.

  1. $63^o$
  2. $35^o$
  3. $27^o$
  4. $59^o$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let the two angles be $a$ and $b$

Then, 
$a  - b = 19$

and, $a + b = \dfrac{890}{9}$

Adding the two equations,

$2a = \dfrac{890 + 19\times 9}{9}$

$2a = \dfrac{1061}{9}$

Thus, $a = \dfrac{1061}{18}$

$a \approx 59^{\circ}$
Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

If two angles of a triangle are acute angles, the third angle:

  1. is less than the sum of the two angles

  2. is an acute angle

  3. is the largest angle of the triangle

  4. may be an obtuse angle
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
For a triangle $ABC$, sum of angles is $180^0$
Two angles are given as acute, $\angle A, \angle B < 90^0$
$\angle A = 90^0 - x$
$\angle B = 90^0 - y$
where, $x,y < 90^0$
$\therefore \angle A + \angle B+ \angle C = 180^0$
$\Rightarrow \angle C = x+y $
$x+y$ can be $>90^0$ or $<90^0$
So, it may be obtuse or acute.
Hence, option D.
Multiple choice maths complementary angle, supplementary angles and adjcent angles acute and obtuse angles types of angle measurement of an angle

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

  1. obtuse angle

  2. straight angle

  3. zero angle

  4. right angle
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

An angle which measure $0^0$ is called zero angle.

An angle which measure more than $0^o$ and less than $90^o$ is an acute angle.
An angle which measures $90^o$ is called a right angle.
An angle which measure more than $90^o$ and less than $180^o$ is an obtuse angle.

Hence, the answer is zero angle.

Multiple choice mathematics and statistics angle and its measurement directed angles

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

  1. True

  2. False

  3. Ambiguous

  4. Data Insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
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

Multiple choice mathematics and statistics angle and its measurement directed angles

If two triangles are congruent, then they are

  1. Symmetrical

  2. Identical

  3. Equilateral

  4. Isosceles
Reveal answer Fill a bubble to check yourself
A Correct answer
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.
Multiple choice mathematics and statistics angle and its measurement directed angles

The angle at a point is

  1. $90^\circ$
  2. $180^\circ$
  3. $300^\circ$
  4. $360^\circ$
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

Multiple choice mathematics and statistics angle and its measurement directed angles

The sum of exterior angles of a triangle is

  1. $180^\circ$
  2. $270^\circ$
  3. $360^\circ$
  4. $540^\circ$
Reveal answer Fill a bubble to check yourself
C Correct answer
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=$360^0$

Multiple choice mathematics and statistics angle and its measurement directed angles

If two angles in a triangle are $ \displaystyle   75^{\circ} $ and $ \displaystyle  95^{\circ} $then the third angle is 

  1. $ \displaystyle 30^{\circ} $
  2. $ \displaystyle 40^{\circ} $
  3. $ \displaystyle 10^{\circ} $
  4. $ \displaystyle 90^{\circ} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle \because $ Sum of the angles in a triangle = $ \displaystyle  180^{\circ} $
i.e. $ \displaystyle 75^{\circ}+95^{\circ}+x=180^{\circ} $
$ \displaystyle \Rightarrow  x=10^{\circ} $

Multiple choice mathematics and statistics angle and its measurement directed angles

Which of the following statements is correct?

  1. A triangle can have two right angles

  2. A triangle can have two obtuse angles
  3. A triangle can have all angles more than $60^{\circ}$

  4. A triangle can have two acute angles
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

As the sum of angles of a triangle is 180 degree therefore first 3 options are ruled out & hence 4th is the answer.

Multiple choice mathematics and statistics angle and its measurement directed angles

Sumit constructed an angle of $90^o$ and trisected it. Measure of two angles taken together will be

  1. $20^o$
  2. $40^o$
  3. $60^o$

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

Trisecting an angle means dividing it in three equal parts.

So if we trisect $90^{\circ}$, we get $3$ equal angles  $30^{\circ}$ each.
On taking two angles together :  $30^{\circ}$+ $30^{\circ}$ =  $60^{\circ}$