Option B:
The value of x is 13 because corresponding angles are congruent.
Solution:
In the given figure line k is parallel to line n, and line p intersects line q at a point located on line n.
Given m∠6 = (2x + 28)° and m∠11 = (6x – 24)°
To find which statement is true for the given details.
Option A: The value of x is 13 because adjacent angles are congruent.
∠6 and ∠11 are not adjacent angles.
Therefore the given statement is false.
Option B: The value of x is 13 because corresponding angles are congruent.
∠6 and ∠11 are corresponding angles.
If two parallel lines cut by a transversal, then the corresponding angles are congruent.
Therefore, m∠6 = m∠11
(2x + 28)° = (6x – 24)°
2x° + 28° = 6x° – 24°
24° + 28° = 6x° – 2x°
52° = 4x°
x = 13°
Therefore the given statement is true.
Option C: The value of x is 55 because adjacent angles are supplementary.
∠6 and ∠11 are not adjacent angles.
Therefore the given statement is false.
Option D: The value of x is 55 because corresponding angles are supplementary.
Corresponding angles are congruent not supplementary.
Therefore the given statement is false.
Option B is correct.
The value of x is 13 because corresponding angles are congruent.
