In a right triangle ABC with right angle at $C$, if $\mathrm{AD}$ is the altitude from vertex $A$ to the hypotenuse $\mathrm{BC}$, which of the following is true about the relationship between the segments $\mathrm{BD}$, $\mathrm{DC}$, and $\mathrm{AD}$?

Given a right triangle where angle $B$ is $152°$, which of the following statements is true?

In triangle CBD, angle CBD has a measure of $140°$. If triangle CBD is a right triangle and angle ABD is the other non-right angle, what is the measure of angle ABD?

Given that $m\angle \mathrm{CED}=72°$ and $m\angle \mathrm{AEB}=7x-2°$, what is the value of $x$ if $m\angle \mathrm{CED}$ and $m\angle \mathrm{AEB}$ are complementary angles?

A right triangle is shown below. Which ratio gives the cosine of $\angle B$?

Given two parallel lines cut by a transversal, if the alternate interior angles are $k-10$ degrees and $2k-40$ degrees, what is the value of $k$?

Given a right triangle with vertices labeled x, z, and w, and angle $xzw$, what is the cosine ratio of angle $xzw$?

A regular polygon with $6$ sides is inscribed in a circle. What is the measure of each interior angle of the polygon?