If the three angles of a quadrilateral are `60^(@), 60^(g) and (5 pi)/(6)` radian. Then, the fourth angle is

Options

A. `60^(@)`
B. `96^(@)`
C. `96^(g)`
D. None of these

Answer

To find the fourth angle of a quadrilateral when three angles are given, we can follow these steps:

### Step 1: Identify the given angles
The three angles of the quadrilateral are:
- Angle 1: \(60^\circ\)
- Angle 2: \(60G\)
- Angle 3: \(\frac{5\pi}{6}\) radians

### Step 2: Convert \(60G\) to degrees
We know that \(1G = 0.9^\circ\). Thus, to convert \(60G\) to degrees:
\[ 60G = 60 \times 0.9^\circ = 54^\circ \]

### Step 3: Convert \(\frac{5\pi}{6}\) radians to degrees
To convert radians to degrees, we use the conversion factor \(\frac{180^\circ}{\pi}\):
\[ \frac{5\pi}{6} \text{ radians} = \frac{5\pi}{6} \times \frac{180^\circ}{\pi} = \frac{5 \times 180}{6} = 150^\circ \]

### Step 4: Sum the known angles
Now we have all angles in degrees:
- Angle 1: \(60^\circ\)
- Angle 2: \(54^\circ\)
- Angle 3: \(150^\circ\)

We can sum these angles:
\[ \text{Sum of known angles} = 60^\circ + 54^\circ + 150^\circ = 264^\circ \]

### Step 5: Calculate the fourth angle
The sum of all angles in a quadrilateral is \(360^\circ\). Therefore, we can find the fourth angle (\(\theta_4\)) by subtracting the sum of the known angles from \(360^\circ\):
\[ \theta_4 = 360^\circ - 264^\circ = 96^\circ \]

### Conclusion
The fourth angle of the quadrilateral is \(96^\circ\).

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