If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
a) an isosceles triangle
b) an obtuse triangle
c) an equilateral triangle
d) a right triangle

Solution:

Given, one angle of a triangle is equal to the sum of the other two angles.

We have to find the type of triangle.

Let us consider a triangle ABC.

Given, ∠A = ∠B + ∠C ---------------- (1)

We know that the sum of all three interior angles of a triangle is always equal to 180

∠A + ∠B + ∠C = 180°

From (1),

∠A + ∠A = 180°

2∠A = 180°

∠A = 180°/2

∠A = 90°

Therefore, the measure of angle A is 90 degrees which implies that the triangle is a right triangle.

✦ Try This: Can two acute angles form a linear pair?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6

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NCERT Exemplar Class 9 Maths Exercise 6.1 Problem 2

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is a) an isosceles triangle, b) an obtuse triangle, c) an equilateral triangle, d) a right triangle

Summary:

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is a right triangle as the measure of one angle is equal to 90 degrees

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