Question

in the figure below, (overline{ab}) is parallel to (overline{ce}). if (angle bae = 34^{circ}), and (angle adc = 104^{circ}), what is the measure of (angle dae)?

Explanation:

Step1: Use the property of parallel lines

Since \( \overline{AB}\parallel\overline{DE}\), then \( \angle BAE=\angle AED = 34^{\circ}\) (alternate - interior angles).

Step2: Apply the angle - sum property of a triangle

In \(\triangle ADE\), we know that the sum of the interior angles of a triangle is \(180^{\circ}\). Let \( \angle DAE=x\).
We know that \( \angle ADC\) is an exterior angle of \(\triangle ADE\). But also, using the angle - sum formula for \(\triangle ADE\): \(x+\angle AED+\angle ADE = 180^{\circ}\). Since \( \angle ADE = 180^{\circ}-\angle ADC\) (linear pair), \( \angle ADE=180 - 104=76^{\circ}\) and \( \angle AED = 34^{\circ}\).
Substitute into \(x+\angle AED+\angle ADE = 180^{\circ}\), we get \(x+34^{\circ}+76^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

\(x=180-(34 + 76)\)
\(x = 70^{\circ}\)

Answer:

G. \(70^{\circ}\)