Given an isosceles triangle ABC with AB = BC and angle B measuring 44°, the angle angle BCD is found to be 112° using the properties of isosceles triangles and linear pairs.
1. Given Information:
- Isosceles triangle ABC with AB = BC.
- angle B measures 44°.
2. Identify the Unknown Angle:
- Let x be the measure of the base angles, angle A and angle C, in the isosceles triangle.
3. Use the Sum of Angles in a Triangle:
- The sum of angles in a triangle is 180°.
- angle A + angle B + angle C = 180.
4. **Set up the Equation:**
- Since angle B is given as 44° and angle A and angle C are equal in an isosceles triangle:
x + 44 + x = 180
5. Solve for x:
- Combine like terms: 2x + 44 = 180.
- Subtract 44 from both sides: 2x = 136.
- Divide by 2: x = 68.
6. Determine the Measure of angle BCD:
- The angles in a straight line (linear pair) add up to 180°.
- angle BCD = 180 - x = 180 - 68 = 112.
Therefore, the measure of angle BCD is 112°.