Question

∠dfg and ∠jkl are complementary angles. ( m angle dfg = x + 2 ), and ( m angle jkl = x - 4 ). find the measure of each angle.

○ ∠dfg = 46, ∠jkl = 54

○ ∠dfg = 46, ∠jkl = 44

○ ∠dfg = 48, ∠jkl = 42

○ ∠dfg = 48, ∠jkl = 52

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \((x + 2)+(x - 4)=90\).

Step2: Simplify the equation

Combine like terms: \(x+x+2 - 4=90\), which simplifies to \(2x-2 = 90\).
Add \(2\) to both sides: \(2x=90 + 2\), so \(2x=92\).
Divide both sides by \(2\): \(x=\frac{92}{2}=46\).

Step3: Find \(m\angle DFG\)

Substitute \(x = 46\) into \(m\angle DFG=x + 2\). Then \(m\angle DFG=46+2 = 48\).

Step4: Find \(m\angle JKL\)

Substitute \(x = 46\) into \(m\angle JKL=x - 4\). Then \(m\angle JKL=46-4 = 42\).

Answer:

\(\angle DFG = 48\), \(\angle JKL=42\) (corresponding to the option \(\angle DFG = 48,\angle JKL = 42\))