## Selina Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles (Including Types, Properties and Constructions)

**Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 26 Triangles (Including Types, Properties and Constructions)**

### Triangles Exercise 26A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.

In each of the following, find the marked unknown angles :

Solution:

Question 2.

Can a triangle together have the following angles ?

(i) 55°, 55° and 80°

(ii) 33°, 74° and 73°

(iii) 85°, 95° and 22°.

Solution:

Question 3.

Find x, if the angles of a triangle are:

(i) x°, x°, x°

(ii) x°, 2x°, 2x°

(iii) 2x°, 4x°, 6x°

Solution:

Question 4.

One angle of a right-angled triangle is 70°. Find the other acute angle.

Solution:

Question 5.

In ∆ABC, ∠A = ∠B = 62° ; find ∠C.

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Question 6.

In ∆ABC, C = 56°C = 56° ∠B = ∠C and ∠A = 100° ; find ∠B.

Solution:

Question 7.

Find, giving reasons, the unknown marked angles, in each triangle drawn below:

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Question 8.

Classify the following triangles according to angle :

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Question 9.

Classify the following triangles according to sides :

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### Triangles Exercise 26B – Selina Concise Mathematics Class 6 ICSE Solutions

Construct traingle ABC, when :

Question 1.

AB = 6 cm, BC = 8 cm and AC = 4 cm.

Solution:

Question 2.

AB = 3.5 cm, AC = 4.8 cm and BC = 5.2 cm.

Solution:

Question 3.

AB = BC = 5 cm and AC = 3 cm. Mea¬sure angles A and C. Is ∠A = ∠C?

Solution:

Question 4.

AB = BC = CA = 4.5 cm. Measure all the angles of the triangle. Are they equal ?

Solution:

Question 5.

AB = 3 cm, BC = 7 cm and ∠B = 90°.

Solution:

Question 6.

AC = 4.5 cm, BC = 6 cm and ∠C = 60°.

Solution:

Question 7.

AC = 6 cm, ∠A = 60“ and ∠C = 45°. Measure AB and BC.

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Question 8.

AB = 5.4 cm, ∠A = 30° and ∠B = 90°. Measure ∠C and side BC.

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Question 9.

AB = 7 cm, ∠B = 120° and ∠A = 30°. Measure AC and BC.

Solution:

Question 10.

BC = 3 cm, AC = 4 cm and AB = 5 cm. Measure angle ACB. Give a special name to this triangle.

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### Triangles Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.

If each of the two equal angles of an isosceles triangle is 68°, find the third angle.

Solution:

Question 2.

One of the angles of a triangle is 110°, the two other angles are equal. Find their value.

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Question 3.

The angles of a triangle are in the ratio 3:5: 7. Find each angle.

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Question 4.

The angles of a triangle are (2x – 30°),(3x – 40°) and (\(\frac { 5 }{ 2 }\)x + 10°) Find the value of x .

Solution:

Question 5.

In each of the following figures, triangle ABC is equilateral and triangle PBC is isosceles. If PBA = 20°; find in each case:

(a) angle PBC.

(b) angle BPC.

Solution:

Question 6.

Construct a triangle ABC given AB = 6 cm, BC = 5 cm and CA = 5.6 cm. From vertex A draw a perpendicular on to side BC. Measure the length of this perpendicular.

Solution:

Question 7.

Construct a triangle PQR, given PQ = 6 cm, ∠P = 60° and ∠Q = 30°. Measure angle R and the length of PR.

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Question 8.

Construct a triangle ABC given BC = 5 cm, AC = 6 cm and ∠C = 75°. Draw the bisector of the interior angle at A. Let this bisector meet BC at P ; measure BP.

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Question 9.

Using ruler and a pair compass only, construct a triangle XYZ given YZ = 7 cm, ∠XYZ = 60° and ∠XZY = 45°. Draw the bisectors of angles X and Y.

Solution:

Question 10.

Using ruler and a pair compass only, construct a triangle PQR, given PQ = 5.5 cm, QR = 7.5 cm and RP = 6 cm. Draw the bisectors of the interior angles at P, Q and R. Do these bisectors meet at the same point ?

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Question 11.

One angle of a triangle is 80° and the other two are in the ratio 3 : 2. Find the unknown angles of the triangle.

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Question 12.

Find the value of x if ∠A = 32°, ∠B = 55° and obtuse angle AED = 115°.

Solution: