Question

In right triangle D, side d is 60, and angle f is 12 degrees less than twice angle e. What is the measure of angle e?

A) 24 degrees

B) 36 degrees

C) 42 degrees

D) 48 degrees

Answer 1

The measure of angle e in right triangle D is 48 degrees (Option D).

Step-by-step explanation:

In a right triangle, the sum of all angles is
`\(90^\circ\)`. Let e represent the measure of angle e. According to the problem, angle f is 12 degrees less than twice angle e, so f = 2e - 12.

The sum of angles e and f in the triangle is equal to
`\(90^\circ\)`, as it is a right triangle. Therefore,
`\(e + f + 90 = 90^\circ\)`. Substituting the expression for f in terms of e, we get
`\(e + (2e - 12) + 90 = 90^\circ\).`

Simplifying the equation, we have
`\(3e - 12 + 90 = 90^\circ\)`, which further simplifies to
`\(3e + 78 = 90^\circ\).` Solving for e, we subtract 78 from both sides, yielding
`\(3e = 12^\circ\).`

Dividing both sides by 3, we find
`\(e = 4^\circ\).` Therefore, the measure of angle e in right triangle D is
`\(4^\circ\)`. However, it's important to note that this answer doesn't match any of the given options (A, B, C, D). This might be an oversight in the question, or there could be a different interpretation of the information provided. Please review the question and options to ensure accuracy.