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Rd Chapter 9 Triangle and its Angles Ex VSAQS Solutions

Question - 1 : - Define a triangle.

Answer - 1 : - Triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.

Question - 2 : - Write the sum of the angles of an obtuse triangle.

Answer - 2 : - The sum of angles of obtuse triangle = 180°.

Question - 3 : - In △ABC, if ∠B = 600, ∠C = 800 and the bisectors of angles ∠ABC and ∠ACB meet at point O, then find the measure of ∠BOC.

Answer - 3 : -

∠B = 600, ∠C = 800 (given)

As per question:

∠OBC = 600/2= 300 and

∠OCB = 800/2= 400

In triangle BOC,

∠OBC + ∠OCB + ∠BOC = 180 0

[Sumof angles of a triangle = 1800]

300 +400 + ∠BOC = 1800

∠BOC = 1100

Question - 4 : - If the angles of a triangle are in the ratio 2:1:3, then find the measure of smallest angle.

Answer - 4 : -

Let angles of atriangles are 2x, x and 3x, where x is the smallest angle.

To find: measure of x.

As, Sum of angles of atriangle = 1800

2x + x + 3x = 1800

6x = 1800

x = 300.Answer

Question - 5 : - If the angles A, B and C of △ABC satisfy the relation B – A = C – B, then find the measure of ∠B.

Answer - 5 : -

Sum of angles of atriangle = 1800

A + B + C = 1800 …(1)

B – A = C – B …(Given)

2B = C + A …(2)

(1) => 2B + B = 1800

3B =1800

Or B = 600

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