A side of the triangle below has been extended to form an exterior angle of 68°. Find the value of x.
Left: 68. Right: 47
Since the exterior angle of a triangle is equal to the sum of the two opposite interior angles, we can conclude that x + 47 + 68 = 180. Simplifying the equation, we get x + 115 = 180. Subtracting 115 from both sides, we find that x = 65. Therefore, the value of x is 65.
wrong.
Apologies for the error. Let's correct it.
Since an exterior angle of a triangle is equal to the sum of the two opposite interior angles, we can conclude that x + 47 + 68 = 180. Simplifying the equation, we get x + 115 = 180. Subtracting 115 from both sides, we find that x = 65. Therefore, the value of x is 65 degrees.
try again.
Apologies for the mistake. Let's try solving it again.
Since the external angle is formed by extending one side of the triangle, it is equal to the sum of the two opposite interior angles.
Let's call the angle opposite to the extended side "x". Therefore, we have:
x + 47 + 68 = 180
Combining like terms, we get:
x + 115 = 180
Subtracting 115 from both sides, we find:
x = 180 - 115
x = 65
So, the value of x is 65 degrees.
To find the value of x, we need to use the properties of triangles and exterior angles.
In a triangle, the sum of the measures of the three interior angles is always 180 degrees.
Given that the left exterior angle is 68 degrees, we know that the corresponding interior angle is 180 - 68 = 112 degrees.
Since we are given that the right interior angle is 47 degrees, we can find the third interior angle by subtracting the sum of the other two from 180 degrees:
Third interior angle = 180 - (112 + 47) = 21 degrees.
Now, let's look at the extended side of the triangle. Since the exterior angle is formed by extending a side of the triangle, it is equal to the sum of the two opposite interior angles.
Therefore, the sum of the left interior angle and the third interior angle is equal to the left exterior angle:
112 + 21 = 133 degrees.
Since the left interior angle is equal to the sum of the left exterior angle and x, we can set up the following equation:
133 + x = 68.
To solve for x, we subtract 133 from both sides:
x = 68 - 133 = -65.
Therefore, the value of x is -65.