Answer: To solve for the value of x and determine the measure of each marked angle, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Here's how to do it:
Set up an equation to solve for x:
The sum of the three angles in a triangle is 180 degrees, so we can write:
(3x + 10) + (3x - 28) + (angle marked as "x") = 180
Simplify the equation:
Combining like terms, we get:
6x - 18 + x = 180
Simplifying further, we get:
7x - 18 = 180
Solve for x:
Adding 18 to both sides, we get:
7x = 198
Dividing both sides by 7, we get:
x = 28
So the value of x is 28.
Determine the measure of each marked angle:
Now that we know x, we can substitute it back into the original expressions for the marked angles:
3x + 10 = 3(28) + 10 = 94
3x - 28 = 3(28) - 28 = 56
So the measures of the marked angles are 94 degrees and 56 degrees, respectively.
Explanation: