Question

The three angles of a triangle are in the ratio of 4 :5:9 calculate the size of the biggest angle

Answer 1

To find the sizes of the angles in a triangle where the angles are in the ratio of 4:5:9, we first need to determine the total sum of the angles in a triangle, which is 180 degrees.

Let the angles be represented as:
- \(4x\) (first angle)
- \(5x\) (second angle)
- \(9x\) (third angle)

The sum of the angles can be written as:
\[
4x + 5x + 9x = 180
\]

Combining the terms gives:
\[
18x = 180
\]

Next, we solve for \(x\):
\[
x = \frac{180}{18} = 10
\]

Now we can find the individual angles:
- First angle: \(4x = 4 \times 10 = 40\) degrees
- Second angle: \(5x = 5 \times 10 = 50\) degrees
- Third angle: \(9x = 9 \times 10 = 90\) degrees

The biggest angle is \(90\) degrees.