Question

∠efg ≅ ∠hfg
a 90
b. 45
c. 18
d. 36

1. use the given information and the diagram to find the value of the variable.

\\( \overrightarrow { a b } \perp \overrightarrow { a d } \\)
a. 6
b. 8
c. 54
d. 90

Explanation:

Step1: Analyze the first problem

Since \(\angle EFG\cong\angle HFG\) and \(\angle EFG+\angle HFG = 180^{\circ}\) (they form a linear - pair), then \(5x+5x=180\).

Step2: Solve the first equation

Combine like terms: \(10x = 180\). Divide both sides by \(10\): \(x=\frac{180}{10}=18\).

Step3: Analyze the second problem

Since \(\overrightarrow{AB}\perp\overrightarrow{AD}\), then \(\angle BAD = 90^{\circ}\). Also, \(\angle BAC+\angle CAD=90^{\circ}\), so \(36 + 9y=90\).

Step4: Solve the second equation

Subtract \(36\) from both sides: \(9y=90 - 36=54\). Divide both sides by \(9\): \(y=\frac{54}{9}=6\).

Answer:

For the first problem (with \(x\)): C. 18
For the second problem (with \(y\)): A. 6