X= 14
The acute angle measures 34 degrees.
The obtuse angle measures 146 degrees.
Step-by-step explanation:
To solve this question, start by solving for x. In order to solve for x, know that angle (10x+6) degrees and angle (3x-8) degrees is a supplementary angle. A supplementary angle is an angle in which the sum of two angles equal 180 degrees.
Since angle (10x+6) degrees and angle (3x-8) degrees is a supplementary angle, we know that the sum of the two angles equal 180 degrees. To find x, write an equation that sets angle (10x+6) degrees and angle (3x-8) degrees equal to 180 degrees. The equation will look like (10x+6) + (3x-8) =180. To start solving the equation, combine like terms, which will look like 13x-2=180. Next, add 2 to both sides, and the equation will look like 13x = 182. Then, divide both sides by 13, and x will equal 14.
Since the x is now known, the actual degrees of the angles can be found. To find the actual degrees of both angles, start by plugging 14 into each angle equation.
For 10x+6, plug 14 into x, and the equation will look like 10(14)+6. Next, simplify the equation, and the answer will be 146 degrees. The 146 degrees is the obtuse angle because an obtuse angle has a measurement greater than 90 degrees but less than 180 degrees.
For 3x-8, plug 14 into x, and the equation will look like 3(14)-8. Next, simplify the equation, and the answer will be 34 degrees.The 34 degrees is the acute angle because acute angles measure less than 90 degrees.
To check if the angles are correct, add both angles, and the answer will equal 180 degrees, which then makes them supplementary angles.
