If a triangle has angles measuring 46 degrees, 51 degrees, and 83 degrees, what type of triangle is it?
a small triangle
b right triangle
c obtuse triangle
d acute triangle
The three angles of the triangle measure 46 degrees, 51 degrees, and 83 degrees. To determine the type of triangle, we need to consider the sum of the angles.
If the sum of the angles in a triangle is 180 degrees, then:
46 + 51 + 83 = 180
Since the sum of the angles is equal to 180 degrees, this triangle is a type of triangle. However, we still need to determine if it is acute, right, or obtuse.
In an acute triangle, all angles are less than 90 degrees.
In a right triangle, one angle is exactly 90 degrees.
In an obtuse triangle, one angle is greater than 90 degrees.
From the given angles, we can see that none of them is equal to or greater than 90 degrees. Therefore, this triangle is an acute triangle.
Answer: d) acute triangle
To determine the type of triangle, we need to analyze the measures of its angles.
In this case, the triangle has angles measuring 46 degrees, 51 degrees, and 83 degrees.
To determine the type of triangle, recall the definitions:
- A small triangle is not a commonly recognized type of triangle, so option a can be eliminated
- A right triangle is a triangle with one right angle (90 degrees). So, if one of the angles is 90 degrees, the triangle is a right triangle. However, none of the given angles is 90 degrees, so option b can be eliminated.
- An obtuse triangle is a triangle with one obtuse angle (greater than 90 degrees). If one of the angles measures more than 90 degrees, the triangle is an obtuse triangle. In this case, the largest angle measures 83 degrees, which is less than 90 degrees. So, we can eliminate option c.
- An acute triangle is a triangle with all three angles measuring less than 90 degrees. If all angles are less than 90 degrees, the triangle is an acute triangle. In this case, all three angles are less than 90 degrees (46, 51, and 83 degrees). Therefore, the triangle is an acute triangle, which means option d is the correct answer.
So, the correct answer is: d) acute triangle.
To determine the type of triangle, we need to analyze the angles:
The angles measuring 46 degrees, 51 degrees, and 83 degrees do not add up to 180 degrees, which is the total angle measure of a triangle. Let's calculate the sum of these angles:
46 + 51 + 83 = 180
Since the sum of the angles equals 180 degrees, we can conclude that this triangle is an acute triangle. Therefore, the correct answer is:
d) acute triangle