An obtuse angle is formed by two adjacent angles, (x−5)° and (3x)°. If the resulting angle is 107°, what is the angle measure of each of the two unknown angles? Round to the nearest whole number.
A: 20° and 87°
B: 28° and 79°
C: 23° and 84°
D: 32° and 75°
As expected, the bot is wrong again.
x-5 + 3x = 107
4x = 112
x = 28
so the angles are 23° and 84°
To find the angle measures of the unknown angles, we can set up an equation based on the information given.
1. We know that an obtuse angle measures more than 90° but less than 180°. Since one of the angles is (x - 5)° and the other angle is (3x)°, we can set up the equation: (x - 5)° + (3x)° = 107°.
2. Simplify the equation: x - 5 + 3x = 107.
3. Combine like terms: 4x - 5 = 107.
4. Add 5 to both sides: 4x = 112.
5. Divide both sides by 4: x = 28.
Now that we have the value of x, we can substitute it back into the original equation to find the angle measures of the unknown angles.
Angle 1: (x - 5)° = (28 - 5)° = 23°.
Angle 2: (3x)° = (3 * 28)° = 84°.
Therefore, the angle measures of the two unknown angles are 23° and 84°.
So the correct answer is C: 23° and 84°.
Haven't you beaten this type of problem to death yet? Surely by now you know how to solve them.
Post your work if you still feel unsure -- but please stop just asking and asking over and over!