Answer:
The value of x is 34.17, and the measures of the angles are approximately 58.34 degrees and 121.68 degrees respectively.
Explanation:
To find the value of x and the measures of the two supplementary angles, we can use the fact that the sum of the angles is equal to 180 degrees since they are supplementary.
So, we set up the equation:
(2x - 10) + (4x - 15) = 180
Combining like terms, we have:
6x - 25 = 180
Adding 25 to both sides of the equation to isolate the variable:
6x = 205
Dividing both sides of the equation by 6:
x = 205/6 = 34.17
Now that we have the value of x, we can substitute it back into the expressions for the angles:
First angle = 2x - 10 = 2(34.17) - 10 = 58.34 degrees
Second angle = 4x - 15 = 4(34.17) - 15 = 121.68 degrees
Therefore, the value of x is 34.17, and the measures of the angles are approximately 58.34 degrees and 121.68 degrees respectively.