A side of the triangle below has been extended to form an exterior angle of 131°. Find the value of xx.
To find the value of x, we know that the sum of the measures of the exterior angles of a triangle is always 360°. Since the exterior angle we're given is 131°, the sum of the other two exterior angles must be 360° - 131° = 229°.
We can see from the diagram that one of the exterior angles (the one adjacent to x) is equal to 90°. So the other exterior angle must be 229° - 90° = 139°.
Since the two exterior angles on the same side of the triangle are supplementary, we can set up the equation:
x + 131° + 139° = 180°
Combining like terms, we get:
x + 270° = 180°
Subtracting 270° from both sides, we find:
x = 180° - 270° = -90°
So the value of x is -90°.
Left: 22. Right: 131.
I apologize for the confusion. If the measure of the exterior angle on the left side is 22° and the measure of the exterior angle on the right side is 131°, we can use the fact that the sum of the measures of the exterior angles of a triangle is always 360°.
Let's call the measure of the third exterior angle x.
We can set up the equation:
22° + x + 131° = 360°
Combining like terms, we get:
x + 153° = 360°
Subtracting 153° from both sides, we find:
x = 360° - 153° = 207°
So the value of x is 207°.