In ∆ ABC above, which of the following could be a value of x?

We can let the vertex of the right angle be D. Thus, triangle BCD is a right triangle with right angle at D. So, angle ABC (with measure 10x) is an exterior angle of triangle BCD and is equal to the sum of angle BDC and angle BCD (recall that an exterior angle of a triangle is equal to the two remote interior angles of the triangle). Since angle BDC is a right angle (90 degrees), angle ABC must be more than 90 degrees. From the answer choices, we see that only choice A (12) would make angle ABC more than 90 degrees.

Alternate Solution:

We can express the angle CBD (where D denotes the vertex of the right triangle) as 180 - 10x.

In a right triangle, the right angle is the greatest; therefore, we must have 180 - 10x < 90, or equivalently, 18 - x < 9. This inequality can be further simplified as x > 9. Only choice A (12) satisfies this requirement.

Answer: A

Bunuel please correct the answer or explain why D is the correct answer choice. Thanks.

The OA is A. Edited. Thank you.

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