Question

In ΔABC, BC is produced to D. ∠A = x + 30°, ∠B = 2x + 25° and ∠ACD = 5x – 5°. Find x and ∠B.

Answer 1

Given: ΔABC with BC extended to D, ∠A = x + 30° ∠B = 2x + 25° ∠ACD = 5x – 5°

Step-wise calculation:

1. Since BC is extended to D at point C, ∠ACD is an exterior angle of ΔABC.

2. By the exterior angle theorem, the exterior angle is equal to the sum of the opposite interior angles.

∠ACD = ∠A + ∠B

3. Substitute the values:

5x – 5 = (x + 30) + (2x + 25)

4. Simplify the right side:

5x – 5 = 3x + 55

5. Move terms to isolate x:

5x – 3x = 55 + 5

2x = 60

6. Solve for x: 

x = 30

7. Find ∠B:

∠B = 2x + 25

= 2(30) + 25

= 60 + 25

= 85°

x = 30° ∠B = 85°