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)
The third angle measure would be 112° because the sum of angles in a triangle is always 180°. The triangle would be classified as an obtuse triangle because it has one angle that is greater than 90°.
Can a triangle have two right angles, and why or why not?
No, a triangle cannot have two right angles. A triangle can only have one right angle. This is because the sum of all angles in a triangle is always 180 degrees. If a triangle had two right angles, that would already be 180 degrees, and there would be no degrees left for the third angle, which is not possible in a triangle.
If a triangle has angles measuring 46° , 51° , and 83° , what type of triangle is it?(
This is an acute triangle. All of its angles are less than 90°.
To find the measure of the third angle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. So, we can subtract the given angles from 180.
180 - 22 - 46 = 112
So, the measure of the third angle is 112 degrees.
Now, let's determine the type of triangle based on the measures of the angles:
- If all angles of a triangle are less than 90 degrees, it is an acute triangle.
- If one angle of a triangle is exactly 90 degrees, it is a right triangle.
- If one angle of a triangle is greater than 90 degrees, it is an obtuse triangle.
In this case, since all three angles (22°, 46°, 112°) are less than 90 degrees, the triangle is an acute triangle.
To find the measure of the third angle in the triangle, we can use the fact that the sum of the angles in any triangle is always 180 degrees.
Let x be the measure of the third angle. We know that one angle measures 22° and another measures 46°. Therefore, we can write the equation:
22° + 46° + x = 180°
Combining the angles, we have:
68° + x = 180°
To solve for x, we subtract 68° from both sides:
x = 180° - 68°
x = 112°
So, the measure of the third angle is 112°.
Now, we can establish the type of triangle based on its angles. Since the third angle measures 112°, which is greater than 90°, we can conclude that this triangle is an obtuse triangle.