Question: If a ray divides an angle into two supplementary angles, then the original angle is a straight angle.
True?
Yes.
If a ray divides an angle into two complementary angles, then the original angle is a right angle.
I know it's true but how do i explain it to my teacher.
You say that you know it is a right angle because a complementary angle is 90 degrees and a right angle is also 90 degrees so that is the answer
If a ray divides an angle into two supplementary angles, then the original angle is a straight angle.
true
True. If a ray divides an angle into two supplementary angles, then the original angle is a straight angle.
To understand why, let's break down the explanation:
1. Definition of Supplementary Angles: Two angles are considered supplementary if their sum is equal to 180 degrees.
2. Ray: In geometry, a ray is a line that starts at a point and extends indefinitely in one direction.
3. Straight Angle: A straight angle is an angle that measures exactly 180 degrees, forming a straight line.
In this scenario, we have an angle that is divided into two supplementary angles by a ray. Let's call the original angle "x" and the supplementary angles "a" and "b".
We know that a + b = 180 degrees because they are supplementary angles.
According to the problem, the ray divides the original angle into two supplementary angles. This means that the original angle "x" is equal to the sum of angles "a" and "b". So, x = a + b.
Substituting the value of a + b = 180 degrees into the equation x = a + b, we have x = 180 degrees.
Since the original angle "x" is equal to 180 degrees, it means the original angle is a straight angle.
Therefore, the statement "if a ray divides an angle into two supplementary angles, then the original angle is a straight angle" is true.