The angles of a triangle are in the ratio of 2 : 3 : 4. The largest angle in the triangle is :

The angles of a triangle are in the ratio of 2 : 3 : 4. The largest angle in the triangle is : ?

Created: 1 year ago | Updated: 2 months ago | Created By:

Ashraful Islam

40 degree

70 degree

75 degree

80 degree

0 20

Institution: Bangladesh Shilpa Bank Ltd Exam: Bangladesh Shilpa Bank Ltd - Officer - 2004
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem of finding the largest angle in a triangle with angles in the ratio of 2:3:4, we first need to remember that the sum of the angles in any triangle is always 180 degrees.

Let's denote the angles of the triangle as 2x, 3x, and 4x, where x is a common multiplier. According to the ratio given:

\[
2x + 3x + 4x = 180
\]

Combining your terms gives:

\[
9x = 180
\]

Now, we can solve for x by dividing both sides by 9:

\[
x = 20
\]

Next, we can find the actual angles by substituting the value of x back into the expressions for the angles:

1. First angle: \(2x = 2 \times 20 = 40\) degrees
2. Second angle: \(3x = 3 \times 20 = 60\) degrees
3. Third angle: \(4x = 4 \times 20 = 80\) degrees

Among these angles, 40, 60, and 80 degrees, the largest angle is clearly 80 degrees. Therefore, the correct answer to the problem is D) 80 degrees.

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