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)^circ), angle d: ((2x + 18)^circ), angle l: ((3z + 11)^circ) (diagrams of angles a, d, l are shown)

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 they're equal)

Substitute \(x = 65\) into \(\angle A\): \(65 - 33 = 32^\circ\). So, \(\angle L = 32^\circ\) (because \(\angle A\) and \(\angle L\) are both supplementary to \(\angle D\), so they're equal).

Step4: Solve for \(z\)

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

Answer:

\(z = 7\)