Answer :
Let's evaluate Oscar's statements and each of the response options step-by-step:
1. Congruent Complementary Angles:
- Complementary angles are defined as two angles whose measures add up to 90 degrees.
- If these two angles are congruent (i.e., they have the same measure), then each angle must be 45 degrees because:
[tex]\[ 2x = 90 \implies x = 45 \][/tex]
- Therefore, Oscar is correct in stating that congruent complementary angles are 45 degrees each.
2. Congruent Supplementary Angles:
- Supplementary angles are defined as two angles whose measures add up to 180 degrees.
- If these two angles are congruent, then each angle must be 90 degrees because:
[tex]\[ 2y = 180 \implies y = 90 \][/tex]
- Therefore, Oscar is also correct in stating that congruent supplementary angles are 90 degrees each.
Hence, Oscar's statement that all congruent complementary angles are 45 degrees each and all congruent supplementary angles are 90 degrees each is correct.
None of the options correctly imply that Oscar's statement is incorrect since:
- The statement "He is not correct, he has the complementary and supplementary angles switched." is false because he accurately described both.
- The statement "He is not correct, you can have 2 angles that add to 90 that are not 45." is irrelevant because the question pertains to congruent angles specifically, which he correctly addressed.
- The statement "He is not correct, you can have 2 angles that add to 180 that are not right." is similarly irrelevant for the same reason.
Conclusion:
Oscar's statement is correct. Therefore, the correct answer is:
- He is correct.
1. Congruent Complementary Angles:
- Complementary angles are defined as two angles whose measures add up to 90 degrees.
- If these two angles are congruent (i.e., they have the same measure), then each angle must be 45 degrees because:
[tex]\[ 2x = 90 \implies x = 45 \][/tex]
- Therefore, Oscar is correct in stating that congruent complementary angles are 45 degrees each.
2. Congruent Supplementary Angles:
- Supplementary angles are defined as two angles whose measures add up to 180 degrees.
- If these two angles are congruent, then each angle must be 90 degrees because:
[tex]\[ 2y = 180 \implies y = 90 \][/tex]
- Therefore, Oscar is also correct in stating that congruent supplementary angles are 90 degrees each.
Hence, Oscar's statement that all congruent complementary angles are 45 degrees each and all congruent supplementary angles are 90 degrees each is correct.
None of the options correctly imply that Oscar's statement is incorrect since:
- The statement "He is not correct, he has the complementary and supplementary angles switched." is false because he accurately described both.
- The statement "He is not correct, you can have 2 angles that add to 90 that are not 45." is irrelevant because the question pertains to congruent angles specifically, which he correctly addressed.
- The statement "He is not correct, you can have 2 angles that add to 180 that are not right." is similarly irrelevant for the same reason.
Conclusion:
Oscar's statement is correct. Therefore, the correct answer is:
- He is correct.
That's right, Andrew! Oscar is **not correct**.
Here's why:
**Congruent complementary angles:**
* **Incorrect:** Complementary angles add up to 90 degrees. If two angles are congruent and complementary, they would each be half of 90 degrees, which is 45 degrees. So, Oscar's statement about congruent complementary angles being 45 degrees is correct.
**Congruent supplementary angles:**
* **Incorrect:** Supplementary angles add up to 180 degrees. If two angles are congruent and supplementary, they would each be half of 180 degrees, which is 90 degrees. So, Oscar's statement about congruent supplementary angles being right angles is incorrect.
So, to sum it up:
* **Congruent complementary angles:** Can be 45 degrees.
* **Congruent supplementary angles:** Can be 90 degrees.
Feel free to ask if you want to explore more angle relationships!
Here's why:
**Congruent complementary angles:**
* **Incorrect:** Complementary angles add up to 90 degrees. If two angles are congruent and complementary, they would each be half of 90 degrees, which is 45 degrees. So, Oscar's statement about congruent complementary angles being 45 degrees is correct.
**Congruent supplementary angles:**
* **Incorrect:** Supplementary angles add up to 180 degrees. If two angles are congruent and supplementary, they would each be half of 180 degrees, which is 90 degrees. So, Oscar's statement about congruent supplementary angles being right angles is incorrect.
So, to sum it up:
* **Congruent complementary angles:** Can be 45 degrees.
* **Congruent supplementary angles:** Can be 90 degrees.
Feel free to ask if you want to explore more angle relationships!
