Apply the Triangle Inequality Theorem to determine if sides with lengths of 3 feet, 4 feet, and 5 feet form a triangle.(1 point)
Responses
Yes, because the sum of any two sides is less than the third side.
Yes, because the sum of any two sides is less than the third side.
Yes, because the sum of any two sides is greater than the third side.
Yes, because the sum of any two sides is greater than the third side.
No, because the sum of any two sides is less than the third side.
No, because the sum of any two sides is less than the third side.
No, because two out of three conditions are met.
Yes, because the sum of any two sides is greater than the third side.
If a right triangle has an angle that is 65°, what is the third angle in the triangle?(1 point)
To find the third angle in a triangle, we need to subtract the sum of the other two angles from 180° (since the sum of the angles in a triangle is always 180°).
In this case, if one angle is 90° (since it is a right triangle), and another angle is 65°, we can calculate the third angle as follows:
Third angle = 180° - (90° + 65°)
Third angle = 180° - 155°
Third angle = 25°
Therefore, the third angle in the triangle is 25°.
What is the measure of the exterior angle x? (1 point
top part 37 bottom side is 42. other side is x of a triangle
To find the measure of the exterior angle, we need to use the property that the measure of an exterior angle of a triangle is equal to the sum of its two remote interior angles.
In this case, we know one of the remote interior angles is 37°. Let's denote the other remote interior angle as y.
The sum of the measures of the exterior angle and the remote interior angles is equal to 180°.
So, x + 37° + y = 180°.
Now, we need to find y. Since the sum of the angles in a triangle is 180°, we can use that knowledge to find y:
37° + 42° + y = 180°.
Adding the known angles together, we have:
79° + y = 180°.
Subtracting 79° from both sides, we get:
y = 180° - 79° = 101°.
Now, we can substitute the value of y back into the equation for the exterior angle:
x + 37° + 101° = 180°.
Combining like terms, we have:
x + 138° = 180°.
Subtracting 138° from both sides, we get:
x = 180° - 138° = 42°.
Therefore, the measure of the exterior angle x is 42°.
Use the figure to answer the question.
A rightward inclined transversal passes through two horizontal parallel lines labeled upper S and upper T. Angles formed at the intersection point of line upper S are labeled clockwise from the top: 1, 2, 4, and 3. Corresponding angles formed at the intersection point of line upper N are labeled clockwise from the top: 5, 22 degrees, 7, and 6.
In the picture, one angle is labeled 22° and lines S and T are parallel. Which other three angles will be 22°? Separate each angle number with a comma.
(1 point)
angles
In this case, we can see that angles 2 and 6 are corresponding angles, which means they are congruent. Thus, angle 2 is also 22°.
Additionally, angles 3 and 7 are alternate interior angles, which are formed by the transversal intersecting parallel lines. Therefore, angle 3 is also 22°.
Hence, the remaining three angles that will be 22° are angles 2, 3, and 6.