If a triangle has a 22° angle and a 46° angle, what can be established about the third angle measure and the type of triangle?(1 point)ResponsesThe third angle measure is 112°, and the triangle is an acute triangle. The third angle measure is 112 degrees , and the triangle is an acute triangle. The third angle measure is 68°, and the triangle is an obtuse triangle.The third angle measure is 68 degrees , and the triangle is an obtuse triangle.The third angle measure is 128°, and the triangle is an obtuse triangle.The third angle measure is 128 degrees , and the triangle is an obtuse triangle.The third angle measure is 112°, and the triangle is an obtuse triangle.The third angle measure is 112 degrees , and the triangle is an obtuse triangle.
The third angle measure is 112°, and the triangle is an obtuse triangle.
To find the measure of the third angle in a triangle, we can use the fact that the sum of all three angles in a triangle is always 180 degrees.
Given that one angle is 22 degrees and another angle is 46 degrees, we can use the equation:
22 + 46 + third angle = 180
To solve for the third angle, we subtract 22 and 46 from both sides of the equation:
third angle = 180 - 22 - 46
third angle = 112 degrees
So, the measure of the third angle is 112 degrees.
Now, let's determine the type of triangle.
An acute triangle is a triangle where all three angles are less than 90 degrees.
In this case, since all three angles (22, 46, and 112) are less than 90 degrees, the triangle is an acute triangle.
Therefore, the correct answer is:
The third angle measure is 112 degrees, and the triangle is an acute triangle.
To find the measure of the third angle in the triangle, we subtract the sum of the other two angles (22° + 46° = 68°) from 180°. This gives us the third angle measure of 180° - 68° = 112°.
Since the third angle measure is 112°, we can establish that the triangle is an obtuse triangle.
Can a triangle have two right angles, and why or why not?(1 point)ResponsesYes, because it would be a right triangle.Yes, because it would be a right triangle.No, because a triangle must have an obtuse angle.No, because a triangle must have an obtuse angle.No, because there needs to be a third angle.No, because there needs to be a third angle.Yes, because 90 + 90 = 180.Yes, because 90 plus 90 equals 180 .
No, a triangle cannot have two right angles.
In a triangle, the sum of all three angles must always be 180 degrees. If a triangle had two right angles, each measuring 90 degrees, the sum of the angles would be 90 + 90 = 180 degrees.
However, having two right angles would mean that the third angle is 0 degrees, resulting in a degenerate triangle, which is not considered a valid triangle.
Therefore, a triangle can have at most one right angle, but it cannot have two right angles.
Can a triangle have two right angles, and why or why not?(1 point)ResponsesYes, because it would be a right triangle.Yes, because it would be a right triangle.No, because a triangle must have an obtuse angle.No, because a triangle must have an obtuse angle.No, because there needs to be a third angle.No, because there needs to be a third angle.Yes, because 90 + 90 = 180.
No, a triangle cannot have two right angles.
In Euclidean geometry, the sum of the angles in a triangle is always 180 degrees. If a triangle had two right angles, each measuring 90 degrees, the sum of the angles would be 90 + 90 = 180 degrees. However, this scenario would imply that there is no remaining angle for the triangle.
Therefore, a triangle cannot have two right angles as it violates the property that the sum of the angles in a triangle is always 180 degrees.
If a triangle has angles measuring 46° , 51° , and 83° , what type of triangle is it?(1 point)Responsesacute triangleacute trianglesmall trianglesmall triangleright triangleright triangleobtuse triangle
To determine the type of triangle, we need to analyze the measures of the angles.
An acute triangle is a triangle where all three angles are less than 90 degrees. In this case, none of the angles (46°, 51°, and 83°) exceed 90 degrees. Therefore, the triangle is an acute triangle.
So, the correct answer is:
The triangle is an acute triangle.