Answer:
x = 100
Explanation:
Supplementary angles add up to 180 degrees, so we can set up the equation:
(1/2x) + (x + 30) = 180
To solve for x, we can start by simplifying the left side of the equation by combining the terms:
(1/2x) + x + 30 = 180
Multiplying both sides of the equation by 2 to eliminate the fraction:
1x + 2(x + 30) = 360
Simplifying the right side of the equation:
1x + 2x + 60 = 360
Combining like terms:
3x + 60 = 360
Subtracting 60 from both sides of the equation:
3x = 300
Dividing both sides of the equation by 3:
x = 100
Therefore, the value of x is 100.
Further explanation:
Supplementary angles are two angles whose sum is 180 degrees. Let's use this fact to form an equation with the given measures:
(1/2x) + (x+30) = 180
To solve for x, we need to isolate it on one side of the equation. Let's start by simplifying the left side:
1/2x + x + 30 = 180
3/2x + 30 = 180
3/2x = 150
x = 100
Therefore, the value of x is 100. To check this result, we can substitute x=100 into the original measures:
(1/2x) = 50
(x+30) = 130
And indeed, 50 and 130 are supplementary angles whose sum is 180.