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