Migher Order Thinking Nina says she
can make a nght angle with an acute
angle and an obtuse angle that have
a common ray. Is Nina correct? Draw a
picture and explain.

Question

Migher Order Thinking Nina says she can make a nght angle with an acute angle and an obtuse angle that have a common ray. Is Nina correct? Draw a picture and explain.

UpStudy AI · Accepted Answer

To determine if Nina is correct, we need to analyze the situation involving an acute angle, an obtuse angle, and a common ray.

### Definitions:
1. **Acute Angle**: An angle that measures less than $$90^\circ$$.
2. **Obtuse Angle**: An angle that measures more than $$90^\circ$$ but less than $$180^\circ$$.
3. **Right Angle**: An angle that measures exactly $$90^\circ$$.

### Explanation:
If we have an acute angle $$A$$ and an obtuse angle $$B$$ that share a common ray, we can visualize this as follows:

1. Let the common ray be $$OA$$.
2. From point $$O$$, draw ray $$OA$$ to form the acute angle $$A$$ with another ray $$OB$$.
3. Now, from point $$O$$, draw ray $$OB$$ to form the obtuse angle $$B$$ with the same ray $$OA$$.

### Drawing:
- Draw a horizontal line for ray $$OA$$.
- From point $$O$$, draw ray $$OB$$ such that it forms an acute angle with ray $$OA$$ (less than $$90^\circ$$).
- Then, draw another ray $$OC$$ such that it forms an obtuse angle with ray $$OA$$ (greater than $$90^\circ$$ but less than $$180^\circ$$).

### Conclusion:
When you combine the acute angle and the obtuse angle that share a common ray, the total angle formed between the two rays will be greater than $$90^\circ$$ and less than $$180^\circ$$. Therefore, it is not possible to create a right angle (which is exactly $$90^\circ$$) using an acute angle and an obtuse angle with a common ray.

Thus, **Nina is incorrect**.

### Visual Representation:
I will now create a simple drawing to illustrate this concept.

1. Draw ray $$OA$$ horizontally.
2. Draw ray $$OB$$ at an acute angle (less than $$90^\circ$$).
3. Draw ray $$OC$$ at an obtuse angle (greater than $$90^\circ$$).

This will help visualize the relationship between the angles.

However, I cannot create images directly. You can sketch this on paper by following the instructions above.
Nina is incorrect. She cannot form a right angle using an acute angle and an obtuse angle that share a common ray.

Migher Order Thinking Nina says she
can make a nght angle with an acute
angle and an obtuse angle that have
a common ray. Is Nina correct? Draw a
picture and explain.

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