Final answer:
Assuming angles ∠ABD and ∠CBD are supplementary, the value of x that satisfies the given angle measures is 292.
Step-by-step explanation:
To find the value of x, we need to consider the relationship between the angles ∠ABD and ∠CBD. If ABD and CBD are part of the same triangle, or if angle ABD is an external angle to CBD we can set up an equation based on the given expressions for each angle.
If we assume that ∠ABD and ∠CBD are supplementary angles (which sum to 180° because they form a linear pair), we can then set up the following equation:
(0.18x + 51)° + (0.07x + 56)° = 180°
Combining like terms we get:
0.18x + 0.07x + 51 + 56 = 180
0.25x + 107 = 180
Subtracting 107 from both sides gives us:
0.25x = 73
Dividing both sides by 0.25 gives us:
x = 292
Therefore, the value of x that satisfies the given angle measures is 292.