If one angle of a triangle is kept fixed then the measure of the remaining two angles vary inversely with each other. State whether the statement is true (T) or false (F)

Solution:

The statement is False.

Consider a Triangle ABC with angles ∠A, ∠B and ∠C. If we consider ∠A to be constant then we can say that ∠B + ∠C = 180° - ∠A.

Therefore there can be three possibilities:

1) ∠B = ∠C

2) ∠B > ∠C

3) ∠B < ∠C

Since there is a possibility of ∠B = ∠C we can say that it is not necessary that ∠B and∠C vary inversely with each other. In other words, the triangle can be an isosceles triangle in which ∠B = ∠C.

✦ Try This: If in a △ABC ∠A is fixed at 80° then ∠B and ∠C vary in inverse proportion. Is the statement true or false?

If ∠A = 80° then

∠B + ∠C = 180° - ∠A.

∠B + ∠C = 180° - 80°

∠B + ∠C = 100°

There are infinite combinations of angle ∠B and ∠C which will add up to 100°. In all but one combination ∠B and ∠C will vary inversely. That one combination will be when ∠B = ∠C i.e. ∠B = ∠C = 50° when they will not vary inversely.

Hence the statement is False.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13

NCERT Exemplar Class 8 Maths Chapter 10 Problem 53

If one angle of a triangle is kept fixed then the measure of the remaining two angles vary inversely with each other. State whether the statement is true (T) or false (F)

Summary:

If one angle of a triangle is kept fixed then the measure of the remaining two angles vary inversely with each other.The statement is false

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