If the angles of a triangle are in the ratio 2:3:4. Find all the angles of the triangle.
Answers
If the angles of a triangle are in the ratio 2:3:4. Find all the angles of the triangle.
➣ Ratio of the three angles of a triangle = 2:3:4
➣ Let the first angle of the triangle = 2x
➣ Let the second angle of the triangle = 3x
➣ Let the third angle of the triangle = 4x
➣ All the three angles of the triangle
➪ By using Angle Sum Property of the triangle
➪ Sum of angles in a triangle = 180°
⇒ 2x + 3x + 4x = 180°
⇒ 9x = 180°
⇒ x =
⇒ x = 20°
➣ First angle of the triangle = 2x = 2 × 20 = 40°
➣ Second angle of the triangle = 3x = 3 × 20 = 60°
➣ Third angle of the triangle = 4x = 4 × 20 = 80°
➦So, the three angles of the triangle are 40°, 60° and 80°
Concept used
Angle sum property (triangle) : This property is only applicable for triangles. It might be any triangle, equilateral, isosceles or scalene. This property is also applicable for all the types of angle based triangles. All the figures that has three sides and angles should have the sum of their angles as 180°. This is the rule of this concept. If this rule is not accepted by any triangle, then that figure cannot be classified as a triangle. This same rule will be used in this question.
Now, we can find the measurements of each angle.
Measurement of first angle :
Measurement of second angle :
Measurement of third angle :
Hence, all the angles of the triangle are 40°, 60° and 80° respectively.