I really need help with this question :(
A pentagon has two exterior angles that measure (3x), two exterior angles that measure (2x + 22) and an exterior angle that measure (x + 41). If all of these angles have different vertices, what are the measures of the exterior angles of the pentagon?
Sum of exterior angles of any polygon is 360°.
So if we add up all five exterior angles of the pentagon, we have
2(3x)+2(2x+22)+x+41=360°
Solve for x.
never mind my reply,
that should have said 360, not 180
MathMate did it for you.
Thank you very much :D
To find the measures of the exterior angles of the pentagon, we need to use the fact that the sum of all exterior angles of any polygon is always 360 degrees.
In this case, we have two exterior angles that measure (3x), two exterior angles that measure (2x + 22), and one exterior angle that measures (x + 41).
So, we can set up an equation to represent the sum of these angles:
(3x) + (3x) + (2x + 22) + (2x + 22) + (x + 41) = 360
Now, let's solve this equation to find the value of x:
Combine like terms:
8x + 85 = 360
Subtract 85 from both sides:
8x = 275
Divide both sides by 8:
x = 34.375
Now that we have the value of x, we can substitute it back into the expressions for the exterior angles to find their measures:
First exterior angle: 3x = 3 * 34.375 = 103.125
Second exterior angle: 2x + 22 = 2 * 34.375 + 22 = 90.75
Third exterior angle: 2x + 22 = 90.75 (same as the second one)
Fourth exterior angle: 3x = 103.125 (same as the first one)
Fifth exterior angle: x + 41 = 34.375 + 41 = 75.375
So, the measures of the exterior angles of the pentagon are:
103.125 degrees, 90.75 degrees, 90.75 degrees, 103.125 degrees, and 75.375 degrees.
The sum of the 5 exterior angles of a pentagon add up to 180°
How can you make use of this fact in solving your problem?
Let me know what you got.