In a `triangle ABC`, If AB = AC and `angle A = 70` Find `angle B and angle C`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Given Information
We have a triangle ABC where:
- AB = AC (the triangle is isosceles)
- Angle A = 70 degrees

### Step 2: Draw the Triangle
Draw triangle ABC with the following properties:
- Mark points A, B, and C.
- Label sides AB and AC as equal.
- Label angle A as 70 degrees.

### Step 3: Use the Isosceles Triangle Property
Since AB = AC, the angles opposite these sides (angle B and angle C) must be equal. Therefore:
- Angle B = Angle C

### Step 4: Apply the Angle Sum Property of a Triangle
The sum of the angles in any triangle is always 180 degrees. Therefore, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
Substituting the known values:
\[ 70^\circ + \text{Angle B} + \text{Angle C} = 180^\circ \]

### Step 5: Substitute Angle B for Angle C
Since Angle B = Angle C, we can replace Angle C with Angle B in our equation:
\[ 70^\circ + \text{Angle B} + \text{Angle B} = 180^\circ \]
This simplifies to:
\[ 70^\circ + 2 \cdot \text{Angle B} = 180^\circ \]

### Step 6: Solve for Angle B
Now, isolate Angle B:
\[ 2 \cdot \text{Angle B} = 180^\circ - 70^\circ \]
\[ 2 \cdot \text{Angle B} = 110^\circ \]
Dividing both sides by 2 gives:
\[ \text{Angle B} = \frac{110^\circ}{2} = 55^\circ \]

### Step 7: Find Angle C
Since Angle B = Angle C, we have:
\[ \text{Angle C} = 55^\circ \]

### Conclusion
Thus, the angles in triangle ABC are:
- Angle B = 55 degrees
- Angle C = 55 degrees

### Final Answer
- Angle B = 55 degrees
- Angle C = 55 degrees

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