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 mathematics and statistics angle and its measurement directed angles

Mark the correct alternative of the following.
An angle of measure $360^o$ is called?

  1. A zero angle

  2. A straight angle

  3. A reflex angle

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

An angle of measure $360^o$ is called a complete angle. [ Using definition of complete angle]

Multiple choice mathematics and statistics angle and its measurement directed angles

 Angles of a triangle are in the ratio $3 : 4 : 5$. The smallest angle is $45^o$.

  1. True

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

Angles of the triangle are in the ratio $3 : 4: 5$
Let the angles be $3x, 4x$ and $5x$
Sum of the angles of the triangle $= 180$
Thus, $3x + 4x + 5x = 180$
$12x = 180$
$x = 15$
Thus, the angles are $45^{o}, 60^{o}$ and $75^{o}$.

Multiple choice mathematics and statistics angle and its measurement directed angles

Mark the correct alternative of the following.
In a $\Delta ABC$, if $\angle A-\angle B=33^o$ and $\angle B-\angle C=18^o$, then $\angle B=?$

  1. $35^o$
  2. $45^o$
  3. $56^o$
  4. $55^o$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given,

$\angle A-\angle B=33^o$.....(1) and $\angle B-\angle C=18^o$.....(2).
Now subtracting  (2) from (1) we get,
$\angle A-2\angle B+\angle C=15^o$.....(3).
We've, $\angle A+\angle B+\angle C=180^o$....(4).
Now subtracting (4) from (3) we get,
$3\angle B=180^o-15^o$
or, $3\angle B=165^o$
or, $\angle B=55^o$.

Multiple choice mathematics and statistics angle and its measurement directed angles

Which of the following statements is correct?

  1. A triangle has two right angles.
  2. All the angles of a triangle are more than 60$^o$

  3. An exterior angle of a triangle is always greater than the opposite interior angles.
  4. All the angles of a triangle are less than 60$^o$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We know, The interior angles of a triangle always add up to 180.
So,  statement A, B and C is not correct.
(C) An exterior angle of a triangle is always greater than the opposite interior angles.
 is correct
Answer (C) An exterior angle of a triangle is always greater than the opposite interior angles.

Multiple choice mathematics and statistics angle and its measurement directed angles

The measure of an angle which is five times its supplement is

  1. $36^0$
  2. $30^0$
  3. $150^0$
  4. $180^0$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let, required angle is =x

Supplementary angle of x is =${{180}^{0}}-x$

Now, according to question,

$ 5\times x={{180}^{0}}-x $

$ 6x={{180}^{0}} $

$ x={{30}^{0}} $


Hence, this is the answer.

Multiple choice mathematics and statistics angle and its measurement directed angles

To draw an angle of $150^o$ using a pair of compass and ruler ______.

  1. Bisect angle between $120^o$ and $180^o$
  2. Bisect angle between $60^o$ and $120^o$
  3. Bisect angle between $0^o$ and $160^o$

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

To draw an angle of 150° using a pair of compass and 

rule we bisect an angle between 120° and 180° 
$\rightarrow$ Since 120°<150°<180° we bisect angle
     between 120° and 180°

Multiple choice mathematics and statistics angle and its measurement directed angles

If the sum of two angles is equal to an obtuse angle, then which of the following is NOT possible?

  1. One obtuse and one acute angle

  2. One right angle and one acute angle

  3. Two acute angles

  4. Two right angles
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Obtuse angles are those angles whose measure is more than$90°$ but less than $180°$.


Since, sum of two right angles is $90°+90°=180°$.

Hence sum of two right angles can not be an obtuse angle.

Multiple choice mathematics and statistics angle and its measurement directed angles

Choose the correct answers from the alternatives given.
In $\Delta $ABC, the sides AB and AC are produced to P and Q respectively. The bisectors of $\angle PBC  \, and \,  \angle QCB $ intersect at a point 0. then $\angle BOC$ is equal to:

  1. 90- $\frac{1}{2} \angle A$
  2. 90+ $\frac{1}{2} \angle A$
  3. $120^{\circ}$ + $\frac{1}{2} \angle A$
  4. 120 - $\frac{1}{2} \angle A$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

2 $\angle 1 + \angle B = 180^{circ}$         (linear pair)
$\angle 1 = 90^{\circ}-\dfrac{1}{2}\angle B$          (1)
Similarly,
$\angle 2 = 90^{\circ} - \dfrac{1}{2} \angle C$   (2)
$\angle BOC = 180^{circ}-  (\angle 1 + \angle 2)$
=$180^{circ}- [180^{circ}-\dfrac{1}{2}$ ($\angle B + \angle C$)]
=$\dfrac{1}{2}[\angle B + \angle C] = \dfrac{1}{2} (180^{circ} - \angle A) = 90^{circ}-\dfrac{1}{2} \angle A$