Question

question 7 (multiple choice worth 1 points) (02 04r mc) in triangle def, if m∠d is (2x)°, m∠e is (3x - 2)°, and m∠f is (x + 8)°, what is the value of x? 29 31 34 59

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: \((2x)+(3x - 2)+(x + 8)=180\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \((2x+3x+x)+(-2 + 8)=180\).
\(6x+6 = 180\).

Step3: Isolate the variable term

Subtract 6 from both sides of the equation: \(6x+6-6=180 - 6\).
\(6x=174\).

Step4: Solve for \(x\)

Divide both sides by 6: \(\frac{6x}{6}=\frac{174}{6}\).
\(x = 29\).

Answer:

29