Question

refer to the figure. if (mangle bdc=(8x + 12)^{circ}) and (mangle fdb=(12x - 32)^{circ}), find (mangle fde). assume the figure is not drawn to scale.

Explanation:

Step1: Note that ∠BDC and ∠FDB are supplementary

Since ∠BDC and ∠FDB form a straight - line (a linear pair), ∠BDC+∠FDB = 180°.
So, (8x + 12)+(12x−32)=180.

Step2: Combine like - terms

Combine the x - terms and the constant terms: (8x+12x)+(12 - 32)=180, which simplifies to 20x−20 = 180.

Step3: Solve for x

Add 20 to both sides of the equation: 20x−20 + 20=180 + 20, getting 20x=200. Then divide both sides by 20: x = 10.

Step4: Find ∠FDB

Substitute x = 10 into the expression for ∠FDB: ∠FDB=(12x−32)°. So, ∠FDB=(12×10−32)°=(120 - 32)° = 88°.

Step5: Note the relationship between ∠FDB and ∠FDE

Since ∠FDB and ∠FDE are vertical angles, ∠FDE=∠FDB.

Answer:

88°