Answer :
Option A is correct, the required simplified value of the x is given as 35.
In triangle DEF, if m∠D = (2x)°, m∠E = (2x − 4)°, and m∠F = (x + 9)°.
for the triangle sum of the interior angles is equal to 180°.
∠D + ∠E + ∠F = 180
2x + 2x - 4 + x + 9 = 180
5x + 5 = 180
5x = 175
x = 35
Thus, the required simplified value of the x is given as 35.
The sum of the measures of the interior angles of a triangle in Euclidean space is continually 180 stages. This reality is equal to Euclid's parallel postulate. This permits the determination of the degree of the 1/3 perspective of any triangle, given the measure of angles. An exterior perspective of a triangle is an attitude that is a linear pair (and subsequently supplementary) to an indoor angle.
The degree of an exterior perspective of a triangle is the same as the sum of the measures of the 2 indoor angles that aren't adjoining to it; this is the outside perspective theorem. The sum of the measures of the 3 exterior angles (one for every vertex) of any triangle is 360 degrees.
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Final answer:
Given that the sum of the interior angles of a triangle equals 180 degrees, we can set up the equation (2x)°+ (2x − 4)°+ (x 9)° = 180°. Solving this equation for x gives us a result of 36.8, which isn't in the supplied options. The expression for m∠f, '(x 9)°', might contain a typographical error.
Explanation:
We're working with a triangle here, so we can use the fact that the sum of the interior angles in a triangle is always 180 degrees. In mathematical terms, we can write this as (2x)°+ (2x − 4)°+ (x 9)° = 180°.
Now, we simplify this equation by combining like terms. We have 5x - 4 = 180. Then, to solve for x, we add 4 to both sides of the equation to get 5x = 184. Finally, we divide both sides of the equation by 5 to solve for x. We find that x = 36.8 which is not an option under the provided choices.
The student's question might have contained a typographical error with the given expression for m∠f, as '(x 9)°' is not a standard mathematical expression. Please check the expressions for the angles again.
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