$$ A+B+C=180^{\circ} $$ - (I) $$ A+B-C=45^{\circ} $$ - (II) $$ B+C-A=60^{\circ} $$ - (III) Q. find.A,B,C.

Question

UpStudy AI · Accepted Answer

To solve the system of equations:

$$
\begin{cases}
A + B + C = 180^\circ \quad \text{(I)} \
A + B - C = 45^\circ \quad \text{(II)} \
B + C - A = 60^\circ \quad \text{(III)}
\end{cases}
$$

**Step 1: Add Equations (I) and (II)**
$$
(A + B + C) + (A + B - C) = 180^\circ + 45^\circ \
2A + 2B = 225^\circ \
A + B = 112.5^\circ \quad \text{(IV)}
$$

**Step 2: Add Equations (I) and (III)**
$$
(A + B + C) + (B + C - A) = 180^\circ + 60^\circ \
2B + 2C = 240^\circ \
B + C = 120^\circ \quad \text{(V)}
$$

**Step 3: Add Equations (II) and (III)**
$$
(A + B - C) + (B + C - A) = 45^\circ + 60^\circ \
2B = 105^\circ \
B = 52.5^\circ
$$

**Step 4: Substitute $$ B = 52.5^\circ $$ into Equation (IV)**
$$
A + 52.5^\circ = 112.5^\circ \
A = 60^\circ
$$

**Step 5: Substitute $$ B = 52.5^\circ $$ into Equation (V)**
$$
52.5^\circ + C = 120^\circ \
C = 67.5^\circ
$$

**Final Solution:**
$$
A = 60^\circ, \quad B = 52.5^\circ, \quad C = 67.5^\circ
$$

Answer:
After simplifying, the angles are A = 60°, B = 52.5°, and C = 67.5°.
A = 60°, B = 52.5°, C = 67.5°

- (I)
- (II)
- (III)
Q. find.A,B,C.

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Trigonometry Questions

- (I) - (II) - (III) Q. find.A,B,C.