explain why an obtuse angle does not have a complement.\nan obtuse angle does not have a complement because…

explain why an obtuse angle does not have a complement.\nan obtuse angle does not have a complement because an angle cannot have a measure of 0°.\nan obtuse angle does not have a complement because the measures of two obtuse angles cannot be added to get 180°.\nthe measure of an obtuse angle is greater than 90°, and cannot be added to the measure of another angle to get 90°.\nthe measure of an obtuse angle is greater than 90°, and you cannot add it to the measure of another obtuse angle and get 180°.

explain why an obtuse angle does not have a complement.\nan obtuse angle does not have a complement because an angle cannot have a measure of 0°.\nan obtuse angle does not have a complement because the measures of two obtuse angles cannot be added to get 180°.\nthe measure of an obtuse angle is greater than 90°, and cannot be added to the measure of another angle to get 90°.\nthe measure of an obtuse angle is greater than 90°, and you cannot add it to the measure of another obtuse angle and get 180°.

Answer

Brief Explanations:

To determine why an obtuse angle has no complement, we first recall the definition of complementary angles: two angles are complementary if their measures add up to (90^\circ). An obtuse angle is defined as an angle with a measure greater than (90^\circ) and less than (180^\circ) (i.e., (90^\circ < \text{obtuse angle} < 180^\circ)).

Now, suppose an obtuse angle (\theta) (where (90^\circ < \theta < 180^\circ)) had a complement, say (\alpha). By the definition of complementary angles, we would have (\theta+\alpha = 90^\circ). Rearranging this formula to solve for (\alpha), we get (\alpha=90^\circ - \theta). But since (\theta > 90^\circ), substituting (\theta) into the equation for (\alpha) gives (\alpha=90^\circ - \theta < 90^\circ - 90^\circ = 0^\circ). However, the measure of an angle cannot be negative (angles have non - negative measures, typically between (0^\circ) and (180^\circ) for the types we are considering here). So, there is no non - negative angle (\alpha) that can satisfy the complementary angle relationship with an obtuse angle (\theta).

Looking at the options:

  • Option 1: Talks about an angle not having a measure of (0^\circ), which is not relevant to the definition of complementary angles.
  • Option 2: Mentions the sum of two obtuse angles not being (180^\circ), but complementary angles sum to (90^\circ), not (180^\circ) (supplementary angles sum to (180^\circ)), so this is incorrect.
  • Option 3: Says an obtuse angle (greater than (90^\circ)) cannot be added to another angle to get (90^\circ). Since the obtuse angle is already more than (90^\circ), adding any non - negative angle to it will result in a sum greater than (90^\circ), so it can't have a complement. This is correct.
  • Option 4: Talks about the sum of two obtuse angles not being (180^\circ), which is about supplementary angles, not complementary angles, so it is incorrect.

Answer:

The measure of an obtuse angle is greater than (90^\circ), and cannot be added to the measure of another angle to get (90^\circ) (the third option).