Is this triangle acute, obtuse, or right angle if angle R is 82 degrees, angle S is 56 degrees, and angle T is 42 degrees?

To determine the type of triangle based on its angles, we need to analyze the given angles R, S, and T. The angles are:

• Angle R = 82 degrees
• Angle S = 56 degrees
• Angle T = 42 degrees

First, we add the angles together:

82 + 56 + 42 = 180 degrees

Since the sum of the angles is 180 degrees, this confirms that we do indeed have a valid triangle.

Next, we evaluate the nature of the triangle based on the individual angles:

• An acute triangle has all angles less than 90 degrees.
• An obtuse triangle has one angle greater than 90 degrees.
• A right triangle has exactly one angle that is exactly 90 degrees.

We can see that:

• Angle R = 82 degrees (acute)
• Angle S = 56 degrees (acute)
• Angle T = 42 degrees (acute)

Since all angles are less than 90 degrees, the triangle is acute.

In conclusion, this triangle is classified as an acute triangle.