The sum of the three interior angles of a triangle is $\displaystyle 180$ degrees.

The interior angles of a triangle must have measures whose sum is $\displaystyle 180^{\circ }$, so the measure of the third angle must be $\displaystyle 180 - (50+45) = 85^{\circ }$.

By the Triangle Exterior-Angle Theorem, an exterior angle of a triangle measures the sum of its remote interior angles; therefore, to get the greatest measure of any exterior angle, we add the two greatest interior angle measures: $\displaystyle 50+85= 135^{\circ }$

Since the angles are supplementary, their sum is 180 degrees.  Because they are in a ratio of 1:4, the following expression could be written:

$\displaystyle x+4x=180$

$\displaystyle 5x=180$

$\displaystyle x=36^{\circ}$

Since the sum of the angles of a triangle is $\displaystyle 180^{\circ}$, and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be $\displaystyle x$, then the following expression could be written:

$\displaystyle x+3x+5x=180$

$\displaystyle 9x=180$

$\displaystyle x=20$

If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.

The angles in a triangle sum to 180 degrees. This makes the middle angle 60 degrees.

The measure of $\displaystyle \angle2$ is twenty degrees greater than the measure $\displaystyle x$ of $\displaystyle \angle 1$, so its measure is 20 added to that of $\displaystyle \angle 1$ - that is, $\displaystyle x + 2 0$.

The measure of $\displaystyle \angle 3$ is thirty degrees less than twice that of $\displaystyle \angle 1$. Twice the measure of $\displaystyle \angle 1$ is $\displaystyle 2x$, and thirty degrees less than this is 30 subtracted from $\displaystyle 2x$ - that is, $\displaystyle 2x-30$.

The sum of the measures of the three angles of a triangle is 180, so, to solve for $\displaystyle x$ - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

$\displaystyle x + (x+20) + (2x-30) = 180$

The measure of $\displaystyle \angle2$ is forty degrees less than the measure $\displaystyle x$ of $\displaystyle \angle 1$, so its measure is 40 subtracted from that of $\displaystyle \angle 1$ - that is, $\displaystyle x -40$.

The measure of $\displaystyle \angle 3$ is ten degrees less than twice that of $\displaystyle \angle 1$. Twice the measure of $\displaystyle \angle 1$ is $\displaystyle 2x$, and ten degrees less than this is 10 subtracted from $\displaystyle 2x$ - that is, $\displaystyle 2x-10$.

The sum of the measures of the three angles of a triangle is 180, so, to solve for $\displaystyle x$ - thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:

$\displaystyle x + (x-40) + (2x - 10) = 180$

The sum of the three angles of a triangle add up to 180 degrees.  Subtract 64 degrees to determine the third angle.

$\displaystyle 180-64= 116$

A right angle has a measure of $\displaystyle 90$^{\circ}$$.  One fifth of the angle is:

$\displaystyle \angle A=\frac{90}{5}= 18$^{\circ}$$

To find the other angle, subtract the given angle from $\displaystyle 90$^{\circ}$$ since complementary angles add up to $\displaystyle 90$^{\circ}$$.

The complementary is:

$\displaystyle \angle 90-\angle65 = \angle25$