If angle a in the diagram equals 45 degrees and angle b is 4x + 5 degrees, determine the value of x.

x = 10.

Step-by-step explanation:

Given : If angle A in the diagram equals 45 degrees and angle B is 4x + 5 degrees,

To find : Determine the value of x.

Solution : We ave given

Angle A = 45 degrees.

Angle B =  4x + 5 .

In the diagram Angle A and B are vertical opposite angle  

Vertical opposite are always equal.

So, Angle A = Angle B

45 = 4x +5.

Now subtract both sides both by 5.

45 -5 = 4x .

40 = 4x .

On dividing both sides by 4.

x = 10.

Therefore, x = 10.