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Answer :
Final answer:
The numerical sum of the degree measures of angles DEA and AEB is 180 degrees. It is derived by solving the given equations for x, substituting x = 15 into the expressions for these angles, and adding them.
Explanation:
In mathematics, when two lines intersect, the opposite angles (also called vertical angles) created by the intersection are equal. Given that ∠AED = x + 25 and ∠AEB = 9x + 10, we can deduce the value of x.
Since ∠AED and ∠AEB form a straight line, their sum is 180 degrees. Therefore, (x + 25) + (9x + 10) = 180. Solving for x we get x = 15 degrees.
The sum of ∠DEA and ∠AEB can be determined by substituting the value of x into their expressions. This will give us: (15 + 25) + (9*15 + 10), summing to 180 degrees.
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