In the adjoining figure, AOB is a straight line. If $x:y:z=4:5:6$ , then $y=$ 

In the adjoining figure, it is given that AOB is a straight line, and the angles are represented by x, y, and z such that:

x : y : z = 4 : 5 : 6

Since AOB forms a straight line in the adjoining figure, the total sum of the angles is:

x + y + z = 180°

Now, the given ratio x : y : z can be expressed as fractions of the total sum:

Sum of the ratio = 4 + 5 + 6 = 15

We calculate each angle using this ratio:

• x = (4/15) × 180° = 48°
• y = (5/15) × 180° = 60°
• z = (6/15) × 180° = 72°

Thus, in the adjoining figure, the values of the angles are determined as follows:

• Angle x: 48°
• Angle y: 60°
• Angle z: 72°

In conclusion, in the adjoining figure, the value of y is 60°.