Question

Someone please help!

Answer 1

1. 37.5°
2. 65°
3. 90°
4. 28

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