# DAV Class 6 Maths Chapter 12 Brain Teasers Solutions

The DAV Maths Book Class 6 Solutions and DAV Class 6 Maths Chapter 12 Brain Teasers Solutions of Triangles offer comprehensive answers to textbook questions.

## DAV Class 6 Maths Ch 12 Brain Teasers Solutions

Question 1.
A. Tick (✓) the correct answer.
(a) Which of the following can be angles of a triangle?
(i) 40°, 30°, 45°
(ii) 35°, 50°, 70°
(iii) 65°, 100°, 95°
(iv) 30°, 55°, 95°
(iv) 30°, 55°, 95°
Sum of three angles 30°, 55° and 95° is 180°.

(b) Two equal angles of a triangle are of measure 70° each. The measure of third angle is:
(i) 20°
(ii) 50°
(iii) 40°
(iv) 60°
(iii) 40°.
70° + 70° + x = 180°
140° + x = 180°
.-. x = 180° – 140° = 40°.

(c) The side opposite to the vertex X of ΔXYZ is ___________
(i) YZ
(ii) XY
(iii) XZ
(iv) YX
(i) YZ. Clearly, YZ is opposite to vertex X.

(d) A triangle can have ___________ exterior angles.
(i) 6
(ii) 4
(iii) 3
(iv) 2
(iii) 3
Exterior angle is formed on producing one of the sides forming the triangle.

(e) Two angles of a triangle are 35° and 50° what type of triangle is this?
(i) Right angled
(ii) Obtuse angled
(iii) Acute angled
(iv) Isosceles
(ii) Obtuse angled
The angle which is more than 90° is called obtuse angle. (a) Name the vertex opposite to side PQ of a ΔPQR.
R
Vertex is opposite to side PQ. (b) How many triangles are there in the given figure? 5.
There are five triangles in the given figure.

(c) All the three sides of a triangle are equal in length. What type of triangle is this?
Equilateral triangle.
An equilateral triangle has three equal sides.

(d) Is it possible to construct a triangle with the segments of length 5 cm, 7 cm, 12 cm? Why?
No, sum of two line segments of a triangle should greater than the third side.

(e) Name the exterior angle formed at the vertex B of the given triangle. ∠CBY.
Angle CBY is the exterior angle of ΔABC on producing side AB to Y.

Question 2.
A, B, C, D are 4 points. Join them in pairs. How many triangles are formed? Number of triangles formed by joining the given points A, B, C and D in pair is ΔABC, ΔBCD, ΔCDA, ΔADB = 4 triangles. Question 3.
Look at the figure and fill in the blanks. (a) 2 triangles having point X in the exterior are ___________ and ___________.
ΔQAR and ΔPTA

(b) 2 triangles which have O as one vertex are ___________ and ___________.
ΔAOT and ΔPOQ

(c) 2 triangles which have PT as one side are ___________ and ___________.
ΔPTA and ΔPTQ

(d) 2 triangles having point Y in their interior are ___________ and ___________.
ΔQSR and ΔQAR

(e) 2 triangles which have A as one vertex are ___________ and ___________
ΔPAQ and ΔQAS Question 3.
Fill in the blanks:
(a) The three ___________ of a triangle are non-collinear.
vertices

(b) Side opposite to the vertex C of ΔABC is ___________
AB

(c) Vertex opposite to the side XZ of ΔXYZ is ___________
Y

(d) The other two angles of a right angled triangle are ___________
acute

(e) Each angle of an equilateral triangle measures ___________
60°

### DAV Class 6 Maths Chapter 12 HOTS

Question 1.
In the given figure, find the sum of Answer:angles ∠A, ∠B, ∠C, ∠D, ∠E, ∠F. In ΔABC,
∠A +∠B + ∠C = 180° …(i)
∠D + ∠E + ∠F = 180° …(ii)
On adding (i) and (ii), we get ∠A + ∠B + ∠C + ∠D + ∠E + ∠F
= 180° + 180°
= 360° Question 2.
Find the values of x and y. Here, x + 40° + 90° – 180°
x + 130° = 180°
∴ x = 180° – 130°
= 50°
Again, y + 45° + 90° = 180°
⇒ y + 135° = 180°
∴ y = 180° – 135°
= 45°.

### DAV Class 6 Maths Chapter 12 Enrichment Questions

Question 1.
Find the sum of angles of the given polygon by dividing it into triangles. 900° On dividing the polygon by joining its vertex it gives 5 triangles which makes a total of 5 × 180° = 900°. Question 2.
Compute the value of x, in the following figure. 52°.
Linear pair of
120° = 180° – 120° = 60°
Now, 60° + x° = 112°
[∵ exterior angle = sum of opposite interior angles]
⇒ x° = 112° – 60° = 52°

Question 1.
Look at the figure and complete the statements: (a) Number of all triangles are ___________.
5

(b) Sides opposite to vertex A are ___________ and ___________.
EF and BC

(c) Number of all the line segments is ___________.
12

(d) Triangles with common vertex B are ___________ and ___________.
ΔBFD and ΔBAC

(e) D is the vertex of triangle ___________, ___________ and ___________ .
ΔDEF, ΔBDF and ΔEDC

(f) A is the vertex of triangles ___________ and ___________.
ΔAEF and ΔABC Question 2.
Observe the given figure and answer the following. (a) Name all the exterior angles
(b) Interior opposite angles of ∠PRS
(c) Adjacent interior angle of ∠RQV
(d) Interior opposite angles of ∠TPR
(e) Name the exterior angle formed by QV and QS.
(a) ∠PRS, ∠TPR and ∠VQR
(b) ∠QPR and ∠PQR
(c) ∠PQR
(d) ∠PQR and ∠PRQ
(e) ∠VQR

Question 3.
In which of the following conditions, the construction of the triangle is possible?
(a) Three angles of triangle are 40°, 60°, 80°.
(b) Three angles of triangle are 30°, 80°, 100°.
(c) The lengths of the 3 sides of a triangle are 6 cm, 3 cm, 11 cm.
(d) The three vertices of a triangle are collinear.
(e) The lengths of the three sides of a triangle are 5 cm, 12 cm and 13 cm.
(f) The three vertices of a triangle are non-collinear.
(a) Sum of the three angles is = 40° + 60° + 80° = 180°
Hence the triangle is possible

(b) Sum of the three angles is = 30° + 80° + 100 = 210° > 180°
Hence the triangle is not possible.

(c) Sum of the two smaller sides of the triangle = 6 + 3 = 9 cm
But 9 cm <11 cm
As the sum of two sides is less than the third side.
∴ triangle is not possible.

(d) Triangle is not possible to construct as the three vertices lie on the same straight line.

(e) Sum of two smaller sides = 5 + 12 = 17 cm > 13 cm.
Hence triangle is possible.

(f) Here the three vertices are non collinear
∴ Triangle is possible.

Question 4.
Fill in the blanks:
(a) Sum of all the angles of a triangle is ___________.
180°

(b) Sum of any two sides of a triangle is always ___________ than the third side.
greater

(c) Three vertices of a triangle must be ___________.
non-collinear

(d) The other two angles of a ___________ triangle are acute.
right angled

(e) The sides of a scalene triangle are ___________ in length.