$40^{\circ}$
To solve the problem of finding the difference between the greatest and the smallest angle in a triangle where the angles are in the ratio 2 : 3 : 4, follow these steps:
- Let the angles of the triangle be \(2x\), \(3x\), and \(4x\) because they are in the ratio 2 : 3 : 4.
- We know the sum of all angles in a triangle is \(180^\circ\). Therefore, we can write the equation: \(2x + 3x + 4x = 180^\circ\)
- Simplify the equation: \(9x = 180^\circ\)
- Solve for \(x\): \(x = \frac{180^\circ}{9} = 20^\circ\)
- Now calculate each angle:
- The smallest angle \(= 2x = 2 \times 20^\circ = 40^\circ\)
- The middle angle \(= 3x = 3 \times 20^\circ = 60^\circ\)
- The greatest angle \(= 4x = 4 \times 20^\circ = 80^\circ\)
- Then, find the difference between the greatest and the smallest angle: \(80^\circ - 40^\circ = 40^\circ\)
- The difference between the greatest and smallest angle is \(40^\circ\).
Thus, the correct option is $40^{\circ}$.
Similar Questions
- In $\Delta PQR$, QR is extended up to S, so that RS = RP. If $\angle RPQ = 55^\circ$ and $\angle PRS = 110^\circ$, then find the measure of $\angle PQS$.
- In a triangle, if angle $A = 30^\circ$ and angle $B = 45^\circ$, then what is the angle of C?
- The total measure of angles in a triangle is:
- ABC is a triangle. BI and CI are angle bisectors of $\angle ABC$ and $\angle ACB$. $\angle BAC = 45^\circ$. Find the measure of $\angle BIC$.
- A side of the triangle is 15 cm and the height of the triangle from this side is 6 cm. Find the area of triangle.
- Area of an equilateral triangle is $49\sqrt{3}\text{ cm}^2$. Find the side of the triangle.
- The perimeter of an equilateral triangle is $36\sqrt{3}$ m. Find the height (in metres).
- Write a Pythagorean triplet whose smallest member is 8.
- The lengths of two sides of a triangle are 7 cm and 8 cm respectively and the measure of the angle included between these two sides is $60^\circ$. The length (in cm) of the third side of the triangle is:
- The lengths of three medians of a triangle are 3 cm, 6 cm and 5 cm. The area of the triangle is:
Important Questions from Triangles
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:
The product of the perimeter of a triangle, the radius of its in‐circle, and a number gives the area of the triangle. The number is
In ∆ABC, 2∠A = 3∠B = 6∠C. What is the value of the largest angle among these three angles?
The longest side in a right-angled triangle is called :
The sum of two sides of a triangle with the third side is
