In the figure, two parallel lines are cut by a transversal. One acute angle is 30°. Find the value of x in the labeled right triangle.
The value of x is 60°.
In the context of a transversal intersecting two parallel lines, angles formed by this intersection are subject to specific angle relationships. Given that one acute angle is 30°, the corresponding angle in the right triangle can be calculated as 60° due to the complementary nature of angles that add up to 90° in a right triangle.
This choice refers to the acute angle already provided in the problem. While it is one of the angles formed by the transversal, it does not represent the value of x in the labeled right triangle. Thus, it cannot be the correct answer, as x must be determined from the relationship between the angles.
This is the correct answer. In a right triangle, one angle is 90°, and the other acute angle, which corresponds to the 30° angle formed by the transversal, must add to 90°. Therefore, 90° - 30° = 60°. This correctly identifies x as 60°.
This choice represents an angle greater than 90°, which cannot exist in a right triangle where one angle is already 90°. Therefore, it is not a valid option for x, as x must be an acute angle that complements the right angle in the triangle.
Similar to choice C, this angle is also obtuse and exceeds 90°. In a right triangle, the angles cannot sum to more than 180°, and since one angle is 90°, the remaining angles must be acute. Thus, this option is not valid for x.
The calculation of x in the labeled right triangle reveals that it measures 60°, derived from the complementary relationship with the provided 30° angle. The correct answer showcases the fundamental properties of angles formed by a transversal intersecting parallel lines, reinforcing the understanding of angle relationships in geometry.
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