Answer:
see explanation
Step-by-step explanation:
Since AB and BC are perpendicular, then
∠ABC = 90° and
∠ABD + ∠DBC = ∠ABC ← substitute values
3r + 5 + 5r - 27 = 90, that is
8r - 22 = 90 ( add 22 to both sides )
8r = 112 ( divide both sides by 8 )
r = 14
Hence
∠ABD = 3r + 5 = (3 × 14) + 5 = 42 + 5 = 47°
∠DBC = 5r - 27 = (5 × 14) - 27 = 70 - 27 = 43°
