7. Non-Right Triangles

Given a circle with radius $r$ = $6$ and an intercepted arc length of $4\pi$, what is the measure of the central angle in radians?

Given two triangles, $△\mathrm{ONM}$ and $△\mathrm{SRQ}$, where side $\mathrm{ON}$ corresponds to $\mathrm{SR}$ and side $\mathrm{NM}$ corresponds to $\mathrm{RQ}$, if $\mathrm{ON}=16$, $\mathrm{NM}=x$, $\mathrm{SR}=20$, and $\mathrm{RQ}=25$, what value of $x$ will make the triangles similar by the SAS similarity theorem?

In parallelogram LMNO, if angle M measures $30°$ and angle N measures $40°$, what is the measure of angle L?

Given triangle $ABC$ with angles $A$, $B$, and $C$, and corresponding opposite sides $a$, $b$, and $c$, which of the following sets of side lengths could represent a triangle according to the Law of Sines?

In triangle $FGH$, an angle bisector from vertex $G$ is perpendicular to side $FH$. If $FG=8$ and $GH=16$, what is the length of $FH$?

Given two right triangles where one leg measures $5$, the hypotenuse measures $13$, and the other leg measures $x$, for the triangles to be congruent by the Hypotenuse-Leg (HL) theorem, what must be the value of $x$?

Which of the following conditions must be true for two right triangles to be congruent by the Hypotenuse-Leg ($\mathrm{HL}$) theorem?

According to the $\mathrm{Law} \mathrm{of} \mathrm{Sines}$, the measure of an exterior angle of a triangle is equal to which of the following measures?

Which of the following sets of angles can be used to construct a triangle?

To prove that two triangles are similar by the SAS similarity theorem, it needs to be shown that two pairs of corresponding sides are in proportion and the included angles are equal. Which of the following statements correctly expresses this condition?

In triangle $ABC$, the measure of angle $A$ is $58°$, and side $a$ is equal to side $c$. What is the measure of angle $C$?

Which of the following statements is true about using the $\mathrm{Law} \mathrm{of} \mathrm{Sines}$ to solve a triangle when given all three side lengths?

Given two parallel lines cut by a transversal, if one of the alternate interior angles measures $m_1=61.8°$, what is the measure of the corresponding alternate interior angle?