Find the Value of a :)

Question

a diagram shows vertical angles where the angle with (4a)° is vertical to the angle with (2b+6)° and the angle with (12b+6)° is vertical to the angle with (8c+5d)°

i tried to explain the diagram as best i could

in the diagram, two lines intersect to form four angles. The measures of the angles are given in terms of the variables a, b, c, and d. I have to find the value of a, and i’m not quite sure how to do it.

Answer 1

Vertical Angle #1: 4a = 2b + 6

Vertical Angle #2: 12b + 6 = 8c + 5d

We can use two of the angles to form supplementary angles. This way we can find the value of b.

(2b + 6) + (12b + 6) = 180

2b + 6 + 12b + 6 = 180

14b + 12 = 180

14b = 168

b = 12

Substitute the 12 for b in order to find the value of a. Therefore, we have the following:

4a = 2(12) + 6

4a = 24 + 6

4a = 30

a = 30/4 = 15/2

The value of a is 15/2 or 7.5.

Answer 2

If I am interpreting your diagram correctly, angle 12b + 6 and 2b + 6 form a linear pair, so

12b + 6 + 2b + 6 = 180

and solving for b, b = 12.

So angle 2b + 6 = 2(12) + 6 = 30.

Since that angle is vertical to 4a, then 4a = 30 and a = 7.5.