Question

in triangle def, if $mangle d=(2x)^{circ}$, $mangle e=(2x - 4)^{circ}$, and $mangle f=(x + 9)^{circ}$, what is the value of x?
35
37
44
71

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(m\angle D+m\angle E + m\angle F=180^{\circ}\).
Substitute the given angle - measures: \((2x)+(2x - 4)+(x + 9)=180\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \((2x+2x + x)+(-4 + 9)=180\), which simplifies to \(5x+5 = 180\).

Step3: Isolate the variable term

Subtract 5 from both sides of the equation: \(5x+5−5=180 - 5\), resulting in \(5x=175\).

Step4: Solve for \(x\)

Divide both sides of the equation by 5: \(\frac{5x}{5}=\frac{175}{5}\), so \(x = 35\).

Answer:

A. 35