The sum of the degree measures of the angles of a quadrilateral is 360. Find the measure of the fourth angle of each quadrilateral given the degree measures of the other three angles.
4x+12, 8x - 10, 6x+5
To find the measure of the fourth angle of the quadrilateral, we need to know the degree measures of the other three angles.
Given the degree measures of the other three angles as:
1st angle: 4x + 12
2nd angle: 8x - 10
3rd angle: 6x + 5
Since the sum of the degree measures of the angles of a quadrilateral is 360, we can write the equation:
(4x + 12) + (8x - 10) + (6x + 5) + fourth angle = 360
Simplifying the equation, let's combine like terms:
18x + 7 + fourth angle = 360
To find the value of x, we can solve for x by subtracting 7 from both sides:
18x + fourth angle = 353
Now, we need more information to solve for the measure of the fourth angle.
To find the measure of the fourth angle of a quadrilateral, you can use the fact that the sum of the degree measures of all four angles is 360 degrees.
Let's use the given degree measures for the other three angles: 4x + 12, 8x - 10, and 6x + 5.
To find the measure of the fourth angle, we need to set up an equation that shows the sum of all four angles equals 360 degrees:
(4x + 12) + (8x - 10) + (6x + 5) + (fourth angle) = 360.
Now, let's solve for the fourth angle.
First, simplify the expression by combining like terms:
18x + 7 + (fourth angle) = 360.
Next, isolate the fourth angle by subtracting 18x + 7 from both sides:
(fourth angle) = 360 - (18x + 7).
Finally, simplify the expression:
(fourth angle) = 360 - 18x - 7.
The measure of the fourth angle of the quadrilateral is 353 - 18x degrees.