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Zorluk: OrtaLines and Angles

In the provided technical drawing, two horizontal parallel lines are intersected by a diagonal transversal line. The measures of two same-side interior angles are given by the expressions (8x−14)∘(8x - 14)^\circ and (6x+26)∘(6x + 26)^\circ. What is the numerical value of xx?

Cevap: 12

Cevap

12
The two angles described are same-side interior angles. Because the lines are parallel, these angles are supplementary and their sum is exactly 180 degrees. Setting up the equation (8x−14)+(6x+26)=180(8x - 14) + (6x + 26) = 180 and solving for xx correctly yields exactly 12.

Adım Adım Çözüm

1
Identify the relationship between the two given angles.
The angles are supplementary.
When two parallel lines are cut by a transversal, same-side interior angles are supplementary, meaning their sum is exactly 180 degrees.
2
Set up an algebraic equation.
(8x−14)+(6x+26)=180(8x - 14) + (6x + 26) = 180
The sum of the measures of the two supplementary angles must equal 180.
3
Combine the like terms on the left side of the equation.
14x+12=18014x + 12 = 180
Adding the variable terms (8x+6x=14x8x + 6x = 14x) and the constant terms (−14+26=12-14 + 26 = 12) simplifies the equation.
4
Isolate the variable term.
14x=16814x = 168
Subtracting 12 from both sides of the equation leaves only the variable term on the left side.
5
Solve for x.
x=12x = 12
Dividing both sides by 14 gives the final numerical value of x.

Anahtar Kavram

Same-side interior angles formed by parallel lines and a transversal are supplementary.
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Konular

Lines and Angles

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