# How are the interior and exterior angles of a triangle related? Question
Non-right triangles and trigonometry How are the interior and exterior angles of a triangle related? 2021-01-24
By the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles (the angles that do not form a linear pair with the exterior angle).
Consider $$\displaystyle\triangle{A}{B}{C}$$ below:
The exterior angle measures $$\displaystyle{m}\angle{A}{C}{D}={110}∘$$ and the two remote interior angles have a sum of $$\displaystyle{m}\angle{A}+{m}\angle{B}={60}∘+{50}∘={110}∘$$. Therefore $$\displaystyle{m}\angle{A}{C}{D}={m}\angle{A}+{m}\angle{B}$$.

### Relevant Questions Are triangles necessarily congruent, is:
1. Each side of one triangle is equal to one of the other triangle's sides.
2. If the two triangles are right and each cathetus of one triangle is equal to a cathetus from the other triangle.
3. If the angles of one triangle are equal to the angles of the other triangle. [Triangle] Determine the measure of each interior angle of △MAN and classify the triangle. m m /trnglMAN is a(n)_______________ triangle. Given a triangle with all angles equal and sides equal to:
1. 3x-5
2. 4x-30
3. 2x+20
Find the value of x. In $$\displaystyle△{P}{Q}{R},{m}∠{P}={46}{x}$$ and $$\displaystyle{m}∠{R}={7}{x}$$,
a. Write and solve an equation to find the measure of each angle.
b. Classify the triangle based on its angles. comprehension check for derivatives of trigonometric functions:
a) true or false: if $$\displaystyle{f}{p}{r}{i}{m}{e}{\left(\theta\right)}=-{\sin{{\left(\theta\right)}}},{t}{h}{e}{n}{f{{\left(\theta\right)}}}={\cos{{\left(\theta\right)}}}.$$
b) true or false: $$\displaystyle{I}{f}\theta$$ is one of the non right angles in a right triangle and ЗІЛsin(theta) = 2/3ZSK, then the hypotenuse of the triangle must have length 3. A triangle is given with one side equal to 18m (a) and angles laying on this side equal to $$\displaystyle{48}^{\circ}$$ (A) and $$\displaystyle{37}^{\circ}$$ (B). Find the ramaining angle (C) and sides (b and c).   A parallelogram with diagonals equal to 56cm and 34cm. The intersect of the angles is $$\displaystyle{120}^{\circ}$$. Find the shorter side's length. 