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Triangles - Aptitude MCQ Questions and Solutions with Explanations

Triangles MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Triangles with easy and logical explanations. Triangles MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-8 section-1

Each section contains 100 MCQs on Triangles .
71
In a triangle ABC, ∠A = 90°, ∠C = 55°, $${AD}$$ ⊥ $${BC}$$. What is the value of ∠BAD ?
Discuss
Answer & Solution
Answer: Option D
Solution:
According to question,
Triangles mcq solution image
In right angle ΔBAC
∠A + ∠B + ∠C = 180°
∠B = 180° - 55° - 90°
∠B = 35°
In right angle ΔADB
∠ADB + ∠ABD + ∠BAD = 180°
∠BAD = 180° - 35° - 90°
∠BAD = 55°
Alternate
ΔBAC ∼ ΔBDA
∴ ∠BCA = ∠BAD = 55°
72
Angle between the internal bisectors of two angles of a triangle ∠B and ∠C is 120°, then ∠A is :
Discuss
Answer & Solution
Answer: Option C
Solution:
According to question,
Triangles mcq solution image
Given : ∠BIC = 120°
∠BIC = 90° + $$\frac{1}{2}$$ ∠A
$$\frac{{\angle A}}{2}$$  = (120° - 90°)
$$\frac{{\angle A}}{2}$$  = 30°
∠A = 60°
73
G is the centroid of the equilateral ΔABC. If AB = 10 cm then length of AG is ?
Discuss
Answer & Solution
Answer: Option B
Solution:
According to question,
Triangles mcq solution image
Given :
AB = BC = CA = 10 cm
G = Centroid
AG = 2 units
GD = 1 unit
AD = 3 units = Height
As we know that the height of the equilateral triangle is
$$\eqalign{ & = \frac{{\sqrt 3 }}{2} \times 10 = 5\sqrt 3 \cr & \therefore 3\,{\text{units}} = 5\sqrt 3 \cr & \,\,\,\,\,\,1\,{\text{unit}} = \frac{{5\sqrt 3 }}{3} \cr & \,\,\,\,\,\,2\,{\text{units}} = \frac{{5\sqrt 3 }}{3} \times 2 \cr & \,\,\,\,\,\,2\,{\text{units}} = \frac{{10\sqrt 3 }}{3} \cr & \therefore {\text{AG}} = \frac{{10\sqrt 3 }}{3}\,cm \cr} $$
74
ABC is a right-angled triangle with AB = 6 cm and BC = 8 cm. A circle with center O has been inscribed inside ΔABC. The radius of the circle is
Discuss
Answer & Solution
Answer: Option B
Solution:
According to question,
Given :
Triangles mcq solution image
AB = 6 cm,         BC = 8 cm
In right angle ΔABC
By using Pythagoras theorem
AC2 = AB2 + BC2
AC2 = 62 + 82
AC2 = 36 + 64
AC2 = 100
AC  = 10 cm
In radius
$$\eqalign{ & = \frac{{a + b - c}}{2} \cr & = \frac{{8 + 6 - 10}}{2} \cr & = \frac{4}{2} \cr & = 2\,cm \cr} $$
75
A point D is taken on the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then
Discuss
Answer & Solution
Answer: Option A
Solution:
According to question,
Triangles mcq solution image
In ΔABC
AB2 = AC2 + BC2 . . . . . . . (i)
ΔACD
AD2 = AC2 + CD2
AC2 = AD2 - CD2 . . . . . . . (ii)
Put the value of AC2 in equation (i)
AB2 = AD2 - CD2 + BC2
AB2 + CD2 = AD2 + BC2
76
ABC is an equilateral triangle and CD is the internal bisector of ∠C. If DC is produced to E such that AC = CE, then ∠CAE is equal to
Discuss
Answer & Solution
Answer: Option D
Solution:
According to question,
Given : ABC is an equilateral triangle CD is the angle bisector of ∠C
Triangles mcq solution image
AC = CE
∴ ∠CAE = ∠CEA
   ∠ACD = 30°
∴ ∠ECA = 180° - 30°
   ∠ECA = 150°
In ΔCAE
   ∠CAE + ∠CEA + ∠ECA = 180°
∴ 2∠CAE = 180° - 150°
   2∠CAE = 30°
   ∠CAE = 15°
77
If each angle of a triangle is less than the sum of the other two, then the triangle is
Discuss
Answer & Solution
Answer: Option B
Solution:
According to question,
In equilateral triangle
Triangles mcq solution image
∠A + ∠B > ∠C
60° + 60° > 60°
120° > 60°
In acute angle triangle
∠P + ∠Q > ∠R
60° + 40° > 80°
100° > 80°
78
In ΔABC and ΔDEF, AB = DE and BC = EF, then one can infer that ΔABC ≅ ΔDEF, when
Discuss
Answer & Solution
Answer: Option D
Solution:
According to question,
Triangles mcq solution image
∠ABC = ∠DEF
Note : Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding sides and the included angles of the other triangle (SAS criterion).
79
In triangle ABC, ∠BAC = 75°, ∠ABC = 45°, $$\overline {BC} $$ is produced to D. If ∠ACD = x°, then $$\frac{x}{3}$$% of 60° is
Discuss
Answer & Solution
Answer: Option D
Solution:
According to question,
Triangles mcq solution image
Given : ∠A = 75°,       ∠B = 45°
∴ ∠ACD = ∠A + ∠B
x° = ∠ACD = 120°
Now, $$\frac{x}{3}$$% of 60° is
= $$\frac{{120}}{3}$$ % of 60°
= 40% of 60°
= $$\frac{{40}}{{100}}$$ × 60°
= 24°
80
The angles of a triangle are in the ratio 2 : 3 : 7. The measure of the smallest angle is :
Discuss
Answer & Solution
Answer: Option A
Solution:
According to question,
Triangles mcq solution image
Let angles are 2x, 3x and 7x
∠A + ∠B + ∠C = 180°
2x + 3x + 7x = 180°
12x = 180°
x = 15°
∴ Smallest angle is = 2 × 15° = 30°