Question

A triangle has angles that measure x, (x + 10), and (2x - 6). Solve for x to find the value of each angle, and determine what type of triangle it is.

Group of answer choices

60, 60, 60. Equilateral

40, 40, 100. Obtuse

44, 46, 90. Right

44, 54, 82. Acute

Answer 1

44, 54, 82. Acute

Explanation:

x + x + 10 + 2x - 6 = 180 (Triangle Sum Theorem)

4x + 4 = 180 (Combine Like Terms)

4x = 176 (Subtraction Property of Equality)

x = 44 (Division Property of Equality)

Now that we have found the value of x, we need to substitute it with the provided angles.

∡1 = x = 44°

∡2 = x + 10 = 54°

∡3 = 2x - 6 = 2(44) - 6 = 82°

So, the answer is an Acute triangle (Option 4).