Question

list the angle measures of δcde in order from smallest to largest. assume that x is a positive number.

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(29x + 71x + 95^\circ = 180^\circ\).

Step2: Solve for \(x\)

Combine like terms: \(100x + 95^\circ = 180^\circ\). Subtract \(95^\circ\): \(100x = 85^\circ\), so \(x = 0.85^\circ\).

Step3: Calculate angle measures

• \(\angle D\) (opposite \(71x\)): \(71x = 71\times0.85 = 60.35^\circ\)
• \(\angle C\) (opposite \(29x\)): \(29x = 29\times0.85 = 24.65^\circ\)
• \(\angle E = 95^\circ\)

Step4: Order angles

Compare \(24.65^\circ\), \(60.35^\circ\), \(95^\circ\). So order is \(\angle C\), \(\angle D\), \(\angle E\).

Answer:

\(m\angle C < m\angle D < m\angle E\) (with \(\angle C = 24.65^\circ\), \(\angle D = 60.35^\circ\), \(\angle E = 95^\circ\))