Question 24

x is 60°

In the given scenario, when two parallel lines are cut by a transversal, corresponding angles are equal. Given that one of the acute angles is 30°, the corresponding angle on the opposite side is also 30°, which allows us to find the value of x in the right triangle.

A) 30°

Option A is incorrect because while there is an acute angle of 30° in the figure, it does not correspond to the value of x we are trying to find. The relationship between angles in the right triangle indicates that x must be different from 30°.

B) 60°

Option B is correct as it represents the angle opposite the 30° angle in the right triangle. Since the sum of the angles in a triangle is 180°, and one angle is 90° (the right angle), the other two angles must sum to 90°. Therefore, 30° + x = 90°, leading to x = 60°.

C) 120°

Option C is incorrect because a triangle cannot have an angle of 120° when it is also required to contain a right angle. The presence of a 90° angle means the maximum for any other angle in the triangle can only be 90°.

D) 150°

Option D is incorrect for similar reasons as Option C. A triangle cannot have an angle of 150° while also containing a right angle, as the other angles would not sum appropriately to 180°.

Conclusion

The value of x is definitively 60° because it is the only angle that complements the given 30° angle in the right triangle while adhering to the triangle sum property. All other options fail to satisfy the essential conditions of triangle angle measurements.