Question

I don’t understand this problem and need help!

Answer 1

see explanation

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°