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in Geometry by (9.2k points)

Can a triangle be formed with the following angles? if yes, name the type of triangle.

(i) 60°, 60°, 60°

(ii) 90°, 55°, 35°

(iii) 60°, 40°, 42°

(iv) 60°, 90°, 90°

(v) 70°, 60°, 50°

(vi) 100°, 50°, 30°

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1 Answer

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by (15.8k points)

(i) 60°, 60°, 60°

Sum of three angles = 60° + 60° + 60° = 180°

Yes, a triangle can be formed.

∴ It is Acute angled triangle. [∵ all the angles < 90°]

(ii) 90°, 55°, 35°.

Sum of three angles = 90° + 55° + 55° = 180°

Yes, a triangle can be formed.

∴ It is a right-angled triangle, [∵ one angle is 90°]

(iii) 60°, 40°, 42°.

Sum of three angles = 60° + 40° + 42° = 142° ≠ 180°

No, The triangle cannot be formed.

(iv) 60°, 90°, 90°.

Sum of three angles = 60° + 90° + 90° = 240° ≠ 180°

∴ No, The triangle cannot be formed. [∵ one angle is > 90°]

(v) 70°, 60°, 50°.

Sum of three angles = 70° + 60° + 50° = 180°

Yes, A triangle can be formed.

∴ It is an acute-angled triangle.

(vi) 100°, 50°, 30°.

Sum of three angles = 100° + 50° + 30° = 180°

Yes, A triangle can be formed.

∴ It is an obtuse-angled triangle.

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