14 The three angles of a triangle are in the ratio \( 1: 3: 5 \). Find the angles.

To find the angles of the triangle in the ratio \(1:3:5\), let's first assign the angles as \(x\), \(3x\), and \(5x\). The sum of the angles in any triangle is always \(180^\circ\). So, we set up the equation: \[x + 3x + 5x = 180^\circ\] Combining like terms, we get: \[9x = 180^\circ\] Now, divide both sides by \(9\): \[x = 20^\circ\] Now we can find each angle: - The first angle: \(x = 20^\circ\) - The second angle: \(3x = 60^\circ\) - The third angle: \(5x = 100^\circ\) Thus, the angles of the triangle are \(20^\circ\), \(60^\circ\), and \(100^\circ\). Here's to geometrical harmony!