GMAT Quantitative Reasoning - DSQ: Calculating an angle in a right triangle

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Given: $\bigtriangleup ABC$ is a right triangle with height $\overline{AD}$ and $\angle A$ is a right angle.

What is the size of $\angle {ABC}$ ?

(1) $\overline{AD}=\overline{DC}$

(2) $\overline{AC}=4$

2

You are given two right triangles: $\triangle ABC$ with right angle , and $\triangle XYZ$ with right angle .

True or false: $\triangle ABC \sim \triangle XYZ$

Statement 1: $\angle A \cong \angle Y$

Statement 2: $\angle B \cong \angle X$

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$\bigtriangleup ABC$ is a right triangle , where $\angle A$ is a right angle, and $\overline{AE}$ is a height of the triangle. What is the measurement of $\angle ABC$ ?

(1) $\angle CAE=30^{\circ}$

(2) $\angle EAB=60^{\circ}$

4

Which interior angle of $\Delta ABC$ has the greatest measure?

Statement 1: $\left (AB \right )^{2} + \left (BC \right )^{2} =\left (AC \right )^{2}$

Statement 2: $\angle B$ is a right angle.

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A right triangle $\bigtriangleup ABC$ with right angle $\angle B$ ; all of its interior angles have degree measures that are whole numbers. What is the measure of $\angle A$ ?

Statement 1: $m \angle A$ is a perfect cube integer.

Statement 2: $m \angle C$ is a multiple of both 7 and 9.

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A right triangle $\bigtriangleup ABC$ with right angle $\angle B$ ; all of its interior angles have degree measures that are whole numbers. What is the measure of $\angle A$ ?