Answer:
- 37.5°
- 65°
- 90°
- 28
Step-by-step explanation:
1. PB is a bisector of ∠ABC, so ∠PBC is 75°/2 = 37.5°.
2. The sum of angles of ΔABC is 180°, so 75° + 40° +∠CAB = 180°. Subtracting 115° from this equation tells you ...
∠CAB = 65°
3. BQ is an altitude of ΔABC, so ∠BQA = 90°. (An altitude always meets the opposite side at a right angle.)
4. BR = RC
2y +8 = 7y -7
15 = 5y . . . . . add 7-2y
3 = y . . . . . . . divide by 5
BC = BR +RC = (2y +8) +(7y -7) = 9y +1 = 9·3 +1 = 28
