In the formula `angleA+angleB+angleC=180^(@)`, if `angleA=90^(@)` and `angle B=55^(@)`, then `angleC=`____________ (a) `pi/4` (b) `pi/6` (c) `pi/3` (d) none of these

Options

A. `pi//4`
B. `pi//6`
C. `pi//3`
D. none of these

Explanation

To solve the problem, we need to find the value of angle C given the values of angle A and angle B. We know that the sum of the angles in a triangle is 180 degrees.

### Step-by-Step Solution:

1. **Write the equation for the sum of angles**:
\[ \text{angle A} + \text{angle B} + \text{angle C} = 180^\circ \]

2. **Substitute the known values**:
Given that angle A = 90° and angle B = 55°, we substitute these values into the equation:
\[ 90^\circ + 55^\circ + \text{angle C} = 180^\circ \]

3. **Combine the known angles**:
Add angle A and angle B:
\[ 145^\circ + \text{angle C} = 180^\circ \]

4. **Isolate angle C**:
To find angle C, subtract 145° from both sides:
\[ \text{angle C} = 180^\circ - 145^\circ \]
\[ \text{angle C} = 35^\circ \]

5. **Convert angle C to radians**:
To convert degrees to radians, we use the conversion factor \(\frac{\pi}{180^\circ}\):
\[ \text{angle C} = 35^\circ \times \frac{\pi}{180^\circ} \]
Simplifying this gives:
\[ \text{angle C} = \frac{35\pi}{180} = \frac{7\pi}{36} \]

6. **Check the options**:
The options provided are:
(a) \(\frac{\pi}{4}\)
(b) \(\frac{\pi}{6}\)
(c) \(\frac{\pi}{3}\)
(d) none of these

Since \(\frac{7\pi}{36}\) does not match any of the options, the correct answer is:
\[ \text{angle C} = \frac{7\pi}{36} \quad \text{(option d: none of these)} \]

### Final Answer:
\(\text{angle C} = \frac{7\pi}{36}\) (d) none of these.

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