Question

The measures of the angles of a triangles are x°,2x°and 3x° resp.Then find the type of that triangle.


A] Acute angled triangle
B] Right angled triangle
C] Obtuse angled triangle
D] Equilateral triangle



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Answer 1

Answer:

Your answer is B] Right angled triangle

Answer 2

Solution:

Measures of the triangle are:

• x°
• 2x°
• 3x°

We know that, the total angle in a triangle is 180°.

So,

x° + 2x° + 3x° = 180°

=> 6x° = 180°

=> x° = 30°

Hence, the angles are:

• x° = 30°
• 2x° = 2 * x° = 2 * 30° = 60°
• 3x° = 3 * 30° = 90°

We observe that the third angle is 90°, which is a right angle.

Hence the triangle is a right angled triangle.

Hence (B) is the answer.

Extra knowledge:

• Acute angled triangle is a triangle in which all the three angles are acute angels i.e, all the angles are less than 90°.
• Obtuse angled triangle is a triangle in which one angle is an obtuse angle i.e, one angle is more than 90° and the other two are acute angles.
• Right angled triangle is a triangle in which one angle is a right angle i.e, in which one angle is equal to 90°.
• Equilateral triangle is a triangle in which all the angles are equal i.e, all the angles are equal to 60°.
• Total angle in a triangle is found using the formula: Total internal angle of a convex polygon = 180(n - 2) where n is the number of sides. For a triangle number of sides = n = 3. So total internal angle = 180(3 - 2) = 180°
• Each interior angle of a regular polygon (all sides of the polygon is equal) = {180(n - 2)}/n where n is the number of sides.
• Total exterior angle of any polygon irrespective of its number of sides = 360°
• Each exterior angle of a regular polygon = 360°/n where n is the number of sides.
• Number of diagonals = {n(n - 3)}/2