The measure of ∠ABD is (0.12x + 61)° and the measure of ∠CBD is (0.13x + 54)°. Find the value of x.

To find the value of ( x ) in the angles ( angle ABD ) and ( angle CBD ), we can start by setting up the equation based on the information given. Since the angles are adjacent and form a straight line, their sum should equal ( 180^circ ).

Here are the steps:

1. Set up the equation:

[

(0.12x + 61) + (0.13x + 54) = 180

]

2. Combine like terms:

[

0.12x + 0.13x + 61 + 54 = 180

]

[

0.25x + 115 = 180

]

3. Subtract ( 115 ) from both sides:

[

0.25x = 180 – 115

]

[

0.25x = 65

]

4. Divide both sides by ( 0.25 ):

[

x = frac{65}{0.25}

]

[

x = 260

]

The value of ( x ) is ( 260 ).

Feel free to ask if you have further questions or need more help!