Answered

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A pair of parallel lines is cut by a transversal.

If [tex]\( m \angle A = (5x - 4)^{\circ} \)[/tex] and [tex]\( m \angle B = (8x - 28)^{\circ} \)[/tex], what is the value of [tex]\( x \)[/tex]?

A. 8
B. 9.4
C. 16.3
D. 36

Sagot :

GinnyAnswer
Let's solve this step-by-step:

Given that [tex]\( \angle A \)[/tex] and [tex]\( \angle B \)[/tex] are corresponding angles formed by a pair of parallel lines cut by a transversal, we know that corresponding angles are equal.

1. Set the measures of the angles equal to each other:
[tex]\[ 5x - 4 = 8x - 28 \][/tex]

2. Rearrange the equation to isolate [tex]\( x \)[/tex]. Start by subtracting [tex]\( 5x \)[/tex] from both sides:
[tex]\[ -4 = 3x - 28 \][/tex]

3. Next, add 28 to both sides to further isolate the term involving [tex]\( x \)[/tex]:
[tex]\[ 24 = 3x \][/tex]

4. Finally, divide both sides of the equation by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 8 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 8 \)[/tex].

So, the correct answer is:
[tex]\[ 8 \][/tex]
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