Question

find the value of x and the missing angle measures.
triangle def with angles: angle d is (4x + 5)°, angle e is (3x - 5)°, angle f is (5x)°.
then spaces for x =, m∠d =, m∠e =, m∠f =

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \((4x + 5) + (3x - 5) + 5x = 180\).

Step2: Simplify the equation

Combine like terms: \(4x + 3x + 5x + 5 - 5 = 180\) → \(12x = 180\).

Step3: Solve for x

Divide both sides by 12: \(x = \frac{180}{12} = 15\).

Step4: Find each angle

• \(m\angle D = 4x + 5 = 4(15) + 5 = 65^\circ\)
• \(m\angle E = 3x - 5 = 3(15) - 5 = 40^\circ\)
• \(m\angle F = 5x = 5(15) = 75^\circ\)

Answer:

\(x = 15\), \(m\angle D = 65^\circ\), \(m\angle E = 40^\circ\), \(m\angle F = 75^\circ\)