In obtuse angle is formed by two adjacent angles with measures x + 10° and 3X if the resultant angle measure is 118 what is the angle measure of each of the two unknown angles round to the nearest whole number
Let's denote the measure of one of the unknown angles as y.
According to the given information, the other unknown angle can be represented as (x + 10°) + y.
Since the angle measure of an obtuse angle is greater than 90°, we can set up the equation: x + 10° + 3x + y > 90°
4x + y + 10° > 90°
Subtracting 10° from both sides: 4x + y > 80°
We are also given that the resultant angle measure is 118°: 4x + y = 118°
Now we have the system of equations:
4x + y > 80°
4x + y = 118°
Next, we solve this system of equations for x and y.
Subtracting the second equation from the first equation:
4x + y - (4x + y) > 80° - 118°
0 > -38°
Since -38° is always true, the inequality 4x + y > 80° does not provide any useful information in solving this problem.
Using the equation 4x + y = 118°, we can solve for x and y.
Subtracting y from both sides of the equation: 4x = 118° - y
Dividing both sides of the equation by 4: x = (118° - y)/4
Since we want the angle measures rounded to the nearest whole number, we can substitute different integers for y, calculate the corresponding values of x, and check if the resultant angle measures add up to 118.
If we take y = 50°, then x = (118° - 50°)/4 = 68°/4 = 17°. This yields angle measures of 17° + 10° = 27° and 3(17°) = 51°. However, these angles do not add up to 118°.
If we take y = 60°, then x = (118° - 60°)/4 = 58°/4 = 14.5°. However, we cannot have a half-degree as an angle measure.
If we take y = 70°, then x = (118° - 70°)/4 = 48°/4 = 12°. This gives us angle measures of 12° + 10° = 22° and 3(12°) = 36°. These angles do not add up to 118°.
By a process of trial and error, we find that if we take y = 68°, then x = (118° - 68°)/4 = 50°/4 = 12.5°. Again, this is not a whole number.
Therefore, there are no whole number solutions that satisfy the given conditions.