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 when lines join trapeziums and kites quadrilaterals and their properties closed figures

Given a trapezium ABCD in which $AB||CD$ and $AD=BC$. If $\angle C=76^{\circ}$, then $\angle D$ equals

  1. $14^{\circ}$
  2. $104^{\circ}$
  3. $76^{\circ}$

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

In trapezium ABCD, $AB \parallel CD$, $AD = BC$
Draw a perpendicular from A on CD to meet CD at M and a perendicular from B on CD to meet at N.
Now, in $\triangle ADM$ and $\triangle BNC$
$\angle AMD = \angle BNC$ (Each $90^o$)
$AM = BN$ (distance between parallel lines)
$AD = BC$ (Given)
Thus, $\triangle ADM \cong \triangle BCN$ (SAS rule)
Hence, $\angle D = \angle C = 76^{\circ}$ (by CPCT)

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

The consecutive angles of a trapezium form an arithmetic sequence. If the smallest angle is $\displaystyle 75^{\circ}$, then the largest angle is

  1. $\displaystyle 100^{\circ}$
  2. $\displaystyle 105^{\circ}$
  3. $\displaystyle 110^{\circ}$
  4. $\displaystyle 115^{\circ}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since, sum of all the four angles of a quadrilateral is $360^o$.

Angle 1 $=75^o$, Angle 2 $=75^o+x$, Angle 3 $=75^o+2x$, Angle 4 $=75^o+3x$
Angle 1 $+$ Angle 2 $+$ Angle 3 $+$ Angle 4 $=360^o$
$\therefore   75^o+75^o+x+75^o+2x+75^o+3x=360^o$
$\Rightarrow 300+6x=360\Rightarrow 6x=60 \Rightarrow x=10$
$\therefore$ Largest angle (Angle 4)$=75^o+3x=75^o+3\times 10=105^o$

Hence, option B.

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

In isoceles trapezoid ABCD, side CD is parallel to to side AB, line segment AC is congruent to line segment BD.The degree measure of angle BDC = $80^o$. Find the measures of the $\angle A$.

  1. $90^o$
  2. $100^o$
  3. $110^o$
  4. $120^o$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

As per the property of isosceles trapezoid, 
Opposite sides of an isosceles trapezoid are the same length (congruent) and the angles on either side of the bases are the same size (congruent).
So, Angle C = $80^o$
Since the top and bottom angles are supplementary, we know that,
Angle A = $180 - 80$
Angle A = $100^o$
Similarly, the Angle of B = $100^o$

Multiple choice

What is the sum of the interior angles of a quadrilateral?

  1. 180 degrees

  2. 270 degrees

  3. 360 degrees

  4. 540 degrees
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sum of the interior angles of any quadrilateral is always 360 degrees.

Multiple choice

What is the name of the theorem that states that the sum of the squares of two sides of a right triangle is equal to the square of the hypotenuse?

  1. Pythagorean Theorem

  2. Euler's Theorem

  3. Fermat's Last Theorem

  4. Goldbach's Conjecture
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean Theorem, also known as Pythagoras' Theorem, is a fundamental theorem in geometry that relates the sides of a right triangle.

Multiple choice

What is the name of the theorem that states that the sum of the angles of a triangle is 180 degrees?

  1. Pythagorean Theorem

  2. Euler's Formula

  3. Triangle Sum Theorem

  4. Law of Cosines
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The Triangle Sum Theorem states that the sum of the angles of a triangle is always 180 degrees.

Multiple choice

What is the name of the theorem that states that the sum of the interior angles of a triangle is equal to 180 degrees?

  1. Brahmagupta's theorem

  2. Pythagorean theorem

  3. Euler's theorem

  4. Triangle Sum Theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Triangle Sum Theorem is a fundamental result in geometry that relates the interior angles of a triangle.

Multiple choice

What is the Pascal triangle?

  1. A triangular array of binomial coefficients

  2. A triangular array of Fibonacci numbers

  3. A triangular array of Catalan numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pascal triangle is a triangular array of binomial coefficients. It is named after Blaise Pascal, who rediscovered it in the 17th century.

Multiple choice

What is the name of the theorem that states that the sum of the interior angles of a triangle is equal to 180 degrees?

  1. Pythagoras' Theorem

  2. Brahmagupta's Theorem

  3. Bhaskara's Theorem

  4. Angle Sum Theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Angle Sum Theorem states that the sum of the interior angles of a triangle is always equal to 180 degrees.

Multiple choice

What is the name of the mathematical concept that describes the relationship between the sides and angles of a right triangle?

  1. Pythagorean Theorem

  2. Trigonometric Functions

  3. Pascal's Triangle

  4. Fermat's Last Theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Multiple choice

What is the name of the mathematical concept that describes the relationship between the sides of a triangle and the angles opposite to them?

  1. Law of Sines

  2. Law of Cosines

  3. Pythagorean Theorem

  4. Trigonometric Functions
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Law of Sines states that in a triangle, the ratio of the sine of an angle to the length of the opposite side is constant.

Multiple choice

What is the name of the theorem that states that the sum of the interior angles of a triangle is equal to 180 degrees?

  1. Brahmagupta's Theorem

  2. Pythagorean Theorem

  3. Euler's Formula

  4. Descartes' Theorem
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Euler's Formula states that the sum of the interior angles of a triangle is equal to 180 degrees.

Multiple choice

What is the name of the theorem that states that the sum of the interior angles of a triangle is equal to 180 degrees?

  1. Brahmagupta's Theorem

  2. Pythagorean Theorem

  3. Euler's Formula

  4. Descartes' Theorem
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Euler's Formula states that the sum of the interior angles of a triangle is equal to 180 degrees.