which of the following statements are true?
a. if two angles form a linear pair, then the angles are supplementary
b. if two angles are right angles, then the angles are complementary
c. if two angles have the same measure, then the angles are congruent.
d. if two angles are supplementary, then the angles are acute.
It is C
I think
Option C) is correct
Because angles can be congreunt only if the measure is same.
I do this on solo mode
I am waiting to hear what you think.
To determine which of the statements are true, we need to understand the definitions and properties of angles.
a. To determine if the statement "if two angles form a linear pair, then the angles are supplementary" is true, we need to know the definition of a linear pair and the definition of supplementary angles.
A linear pair refers to two adjacent angles that together form a straight line, which means they add up to 180 degrees.
Supplementary angles refer to two angles that add up to 180 degrees.
Since the definition of a linear pair is that the angles add up to 180 degrees, statement a is true.
b. To determine if the statement "if two angles are right angles, then the angles are complementary" is true, we need to understand the definition of right angles and complementary angles.
A right angle measures exactly 90 degrees.
Complementary angles refer to two angles that add up to 90 degrees.
Since the definition of a right angle is that it measures 90 degrees, statement b is false. Right angles are not complementary angles.
c. To determine if the statement "if two angles have the same measure, then the angles are congruent" is true, we need to understand the definition of congruent angles.
Congruent angles refer to two angles that have the same measure or size.
Since the statement directly matches the definition of congruent angles, statement c is true.
d. To determine if the statement "if two angles are supplementary, then the angles are acute" is true, we need to understand the definitions of supplementary angles and acute angles.
As mentioned earlier, supplementary angles refer to two angles that add up to 180 degrees.
Acute angles are angles that measure less than 90 degrees.
Since the definition of supplementary angles does not indicate anything about the angles being acute, statement d is false. Supplementary angles can be both acute and obtuse.
To summarize:
- Statement a is true: If two angles form a linear pair, then the angles are supplementary.
- Statement b is false: Right angles are not complementary angles.
- Statement c is true: If two angles have the same measure, then the angles are congruent.
- Statement d is false: Supplementary angles can be acute or obtuse.