Answer:
x = 4 , ∠ B = 77° , ∠ D = 31°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
∠ CBW is an exterior angle of Δ BCD , then
∠ CBW = ∠ BCD + ∠ BDC ( substitute values )
18x + 5 = 46 - 1 + 8x , that is
18x + 5 = 45 + 8x ( subtract 8x from both sides )
10x + 5 = 45 ( subtract 5 from both sides )
10x = 40 ( divide both sides by 10 )
x = 4
substitute x = 4 into the expressions for ∠ B and ∠ D
∠ B = 18x + 5 = 18(4) + 5 = 72 + 5 = 77°
∠ D = - 1 + 8x = - 1 + 8(4) = - 1 + 32 = 31°
