In the figure above, line segments \( \overline{AD} \text{ and } \overline{BE}\) are perpendicular and intersect at point \(C\). Angle \(B\) is congruent to angle \(D\), and the measure of angle \(A\) is \(60\degree\). What is the measure of angle \(D\)?

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Through intuition or by using AA similarity, we can conlude that the two triangles are similar. AA similarity can be determined since we have two pairs of congruent angles: angle \(B\) is congruent to angle \(D\) and \(m \angle ACB = m \angle ECD \) because they are vertical angles. Filling in a few of the given angles:

Because the angles of \(\triangle ABC\) add up to \(180 \degree\), \(m\angle B = 30 \degree \). Since angle \(B\) and \(D\) are congruent, \( m\angle D = 30 \degree \) as well.

Most SAT figures are drawn to scale. Some may include a disclaimer saying otherwise. Even so, the figure will almost always be close to the actual size. Therefore, using intuition to spot similar figures, especially triangles, can give you hints into how to approach the problem.