$40^{\circ}$
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 $\triangle ABC$, $BD \perp AC$ at $D$ and $\angle DBC = 40^\circ$. $E$ is a point on $BC$ such that $\angle CAE = 37^\circ$. What is the measure of $\angle AEB$?
- 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.
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- 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:
Important Questions from Triangles
Among the following options, which are NOT sides of a triangle?
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:
In the equilateral Δ ABC, the base BC is trisected at D and E. The line through D, Parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. If EG and DF intersect at H, then what is the ratio of the sum of the area of parallelogram AGHF and the area of the Δ DHE to the area of the Δ ABC?
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
A man goes 24 m towards east and then 10 m towards north. How far is he away from his initial position?
