Classify each triangle by its angle measures.
A triangle has angles measuring 35 degrees, 118 degrees, and 27 degrees.
A triangle has tick marks on all three sides and three angles all measuring less than 90 degrees.
A triangle has angles measuring 38 degrees, 90 degrees, and 52 degrees.
The second answer is wrong.
It said all angles are less than 90, so it is acute
The bot's answer of obtuse would mean one of the angle is > 90°
Since it has tick marks on all 3 sides, it must be equilateral, with all
angles equal to 60°
and the first answer is also wrong -- scalene and obtuse
A right triangle has acute angles measuring 2x+6 degrees and 3x−26 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.(4 points)
The sum of all angles in a triangle is always 180 degrees.
If the acute angles of the right triangle are 2x+6 and 3x−26, then the measure of the right angle is 90 degrees.
Therefore, we can use the Triangle Angle Sum Theorem to solve for x:
2x+6 + 3x−26 + 90 = 180
5x+70 = 180
5x = 110
x = 22
Now that we know x, we can substitute it back into the expressions for the acute angles to find their measures:
2x+6 = 50 degrees
3x−26 = 28 degrees
So, the acute angles of the right triangle measure 50 and 28 degrees, while the right angle measures 90 degrees.
To classify each triangle by its angle measures, we need to understand the different types of triangles based on their angles.
1. A triangle with angles measuring 35 degrees, 118 degrees, and 27 degrees:
To classify this triangle, we need to compare the angle measures to the standard types of triangles. Here are the options:
- Acute triangle: All angles are less than 90 degrees.
- Obtuse triangle: One angle is greater than 90 degrees.
- Right triangle: One angle is exactly 90 degrees.
Since none of the angles in this triangle are greater than 90 degrees, we can determine that it is an acute triangle.
2. A triangle with tick marks on all three sides and three angles measuring less than 90 degrees:
To classify this triangle, we can apply the same logic as above. Here are the options:
- Acute triangle: All angles are less than 90 degrees.
- Obtuse triangle: One angle is greater than 90 degrees.
- Right triangle: One angle is exactly 90 degrees.
Since all three angles are less than 90 degrees, we can classify this triangle as an acute triangle.
3. A triangle with angles measuring 38 degrees, 90 degrees, and 52 degrees:
Using the same classification criteria, we can determine:
- Acute triangle: All angles are less than 90 degrees.
- Obtuse triangle: One angle is greater than 90 degrees.
- Right triangle: One angle is exactly 90 degrees.
In this case, we have one angle exactly measuring 90 degrees (a right angle), so we can classify this triangle as a right triangle.
Therefore, the classifications of the given triangles based on their angle measures are:
1. Acute triangle
2. Acute triangle
3. Right triangle.
The first triangle is an acute triangle.
The second triangle is an obtuse triangle.
The third triangle is a right triangle.