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 construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle triangle inequality

Sum of the length of any two sides of a triangle is always greater than the length of third side.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.

Multiple choice maths construction of angles identifying angles acute and obtuse angles types of angle

An angle whose measure is the sum of the measures of two right angles is _______.

  1. Acute

  2. Obtuse

  3. Right

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

Measure of a right angle is $90^ \circ$

Measure of a straight angle is $180^ \circ$
Sum of the measure of two right angles is $(90+90)^ \circ=180^ \circ$
Thus an angle whose measure is the sum of two right angles is $Straight$

Multiple choice maths construction of angles identifying angles acute and obtuse angles types of angle

Based on the angle measures given, which triangle is not acute?

  1. $35^\circ,\, 69^\circ,\, 76^\circ$
  2. $60^\circ,\, 60^\circ,\, 60^\circ$
  3. $88^\circ,\, 46^\circ,\, 46^\circ$
  4. $90^\circ,\, 45^\circ,\, 45^\circ$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For acute angles triangle all the three angles must be less than ${ 90 }^{ \circ  }$.

In option $D$ one of the angle is ${ 90 }^{ \circ  }$ , so it is not acute angles triangle.

Multiple choice maths construction of angles identifying angles acute and obtuse angles types of angle

An angle that is $\displaystyle  { 1 }^{ o }$ less than right angle is:

  1. Reflex angle

  2. Straight angle

  3. Obtuse angle

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

Right angle measures $\displaystyle  { 90 }^{ o }$
$\displaystyle  { 1 }^{ o }$ less of right angle = $\displaystyle { 90 }^{ o }-{ 1 }^{ o }$
$\displaystyle { 89 }^{ o }$
Which is an acute 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 construction of angles identifying angles acute and obtuse angles types of angle

If the angle is greater than $\displaystyle { 0 }^{ o }$ and less than $\displaystyle { 90 }^{ o }$, then the angle is known as:

  1. Obtuse angle

  2. Right angle

  3. Acute angle

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

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 construction of angles identifying angles acute and obtuse angles types of angle

The sum of two acute angles can be:

  1. Acute angles

  2. Obtuse angles

  3. Right angles

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let one angle is $\displaystyle { 30 }^{ o }$ and the other angle is $\displaystyle { 40 }^{ o }$ then sum $\displaystyle { 70 }^{ o }$. which is an acute angle.
Let one angle be $\displaystyle { 70 }^{ o }$ and other angle is $\displaystyle { 80 }^{ o }$, then sum is $\displaystyle { 150 }^{ o }$ which is obtuse angle.
Let one angle is $\displaystyle { 45 }^{ o }$ and another angle is $\displaystyle { 45 }^{ o }$ then sum is $\displaystyle { 90 }^{ o }$ which is right angle.

Multiple choice maths construction of angles identifying angles acute and obtuse angles types of angle

Range of an obtuse angle is:

  1. $[0˚, 90˚)$
  2. $(0˚, 90˚]$
  3. $[90˚, 180˚)$
  4. $(90˚, 180˚)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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 $\displaystyle {360 }^{ o }$.