In the given figure, find the value of x.
The question requires us to find the value of angle \( x \) in the given figure, using the linear pair and the sum of angles around a point.
Given angles:
- \(\angle AOB = 35^\circ\)
- \(\angle DOC = 64^\circ\)
Explanation:
- Since \( \angle AOB \) and \( \angle X \) are on a straight line, they form a linear pair. Therefore, their sum is \( 180^\circ \).
- We can express this as a linear equation: \(35^\circ + x + \angle DOC = 180^\circ\)
- Substitute the value of \( \angle DOC = 64^\circ \): \(35^\circ + x + 64^\circ = 180^\circ\)
- Simplifying the equation: \(x + 99^\circ = 180^\circ\)
- Solving for \( x \): \(x = 180^\circ - 99^\circ = 81^\circ\)
- However, since we need to account for the angle around point \( O \), we subtract \( 35^\circ \) from \( 180^\circ\): \(x = 180^\circ - (35^\circ + 29^\circ) = 151^\circ\)
Therefore, the value of \( x \) is \( 151^\circ \).
Hence, the correct answer is: \(151^\circ\)
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