Can a triangle have three angles whose measures are
`(1)/(3)` right angles, 1 right angles, `60^(@)` ?

Answer

To determine if a triangle can have three angles measuring \( \frac{1}{3} \) right angles, 1 right angle, and \( 60^\circ \), we will follow these steps:

### Step 1: Convert the angles to degrees
- A right angle measures \( 90^\circ \).
- Therefore, \( \frac{1}{3} \) of a right angle is calculated as:
\[ \frac{1}{3} \times 90^\circ = 30^\circ \]

### Step 2: List the angles
- Now we have the three angles:
- \( \frac{1}{3} \) right angle = \( 30^\circ \)
- 1 right angle = \( 90^\circ \)
- \( 60^\circ \)

### Step 3: Sum the angles
- We need to check if the sum of these angles equals \( 180^\circ \):
\[ 30^\circ + 90^\circ + 60^\circ = 180^\circ \]

### Step 4: Conclusion
- Since the sum of the angles is \( 180^\circ \), we can conclude that it is possible for a triangle to have angles measuring \( 30^\circ \), \( 90^\circ \), and \( 60^\circ \).

Thus, the answer is **Yes**, a triangle can have three angles whose measures are \( \frac{1}{3} \) right angles, 1 right angle, and \( 60^\circ \).

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