Question

1. three angles are shown with the given information. angle a is supplementary to ∠d. angle l is supplementary to ∠d. what is the value of z? angle a: (x - 33)°, angle d: (2x + 18)°, angle l: (3z + 11)°

Explanation:

Step1: Use supplementary angles property

Supplementary angles sum to \(180^\circ\). So, \(\angle A + \angle D = 180^\circ\). Substitute the expressions: \((x - 33) + (2x + 18) = 180\).

Step2: Solve for x

Combine like terms: \(3x - 15 = 180\). Add 15 to both sides: \(3x = 195\). Divide by 3: \(x = 65\).

Step3: Find \(\angle A\) (or \(\angle L\))

Since \(\angle A\) and \(\angle L\) are both supplementary to \(\angle D\), they are equal. Calculate \(\angle A\): \(65 - 33 = 32^\circ\). So, \(\angle L = 32^\circ\).

Step4: Solve for z

Set \(\angle L = 3z + 11\) equal to \(32^\circ\): \(3z + 11 = 32\). Subtract 11: \(3z = 21\). Divide by 3: \(z = 7\).

Answer:

\(z = 7\)