7. Non-Right Triangles

Given that the major arc $JL$ of a circle measures $300°$, which of the following best describes triangle $JLM$ inscribed in the circle with points $J$, $L$, and $M$ on the circumference?

Point D is the incenter of triangle BCA. If $\angle \mathrm{FDG}$ = $136°$, what is the measure of angle $\angle \mathrm{BCA}$?

Given that an equilateral triangle and an isosceles triangle share a common side, and the triangle $ABC$ is equilateral, what is the measure of angle $\angle ABC$ in degrees?

Given the Law of Sines, could $a$ and $b$ be the side lengths of a triangle if $a=3$ and $b=7$ and the angle opposite $a$ is $80°$ and the angle opposite $b$ is $40°$?

Which of the following pairs of triangles can be proven congruent using the $\mathrm{Law} \mathrm{of} \mathrm{Sines}$?

Given triangle $ABC$ where $A$ and $B$ are on straight lines $l$ and $m$ respectively, and the measure of angle $A$ is $43°$ and angle $B$ is $47°$, what is the measure of angle $y$ (angle $C$) in degrees?

According to the Law of Sines, under which of the following angle conditions could a triangle exist? Select the correct option.

According to the $LawofSines$, which triangles can be mapped onto one another through a sequence of rigid transformations?

$$In the context of the Law of Sines $\mathrm{Law} \mathrm{of} \mathrm{Sines}$ and triangle geometry, if two lines (such as transversals or sides) are not parallel, which types of angles remain congruent?

According to the $\text{Law of Sines}$, which set of angle measures could represent the angles of a triangle?

Which of the following sets of angles can form a triangle?

Quadrilateral RSTU is a parallelogram. If angle R measures $x$ degrees and angle S measures $70$ degrees, what must be the value of $x$?

Given a triangle with sides $a$, $b$, $c$ opposite angles $A$, $B$, $C$ respectively, which equation can be used to find $b$ using the Law of Sines?

Use the Law of Sines to find the length of side $a$ to two decimal places.

Use the Law of Sines to find the angle $B$ to the nearest tenth of a degree.