13. A side of the triangle below has been
extended to for an exterior angle of
161°. Find the value of x.
A. 19°
B. 46°
C. 134°
To find the value of x, we can use the fact that the sum of the exterior angles of any triangle is 360 degrees.
Let's label the angle at the vertex where the extension was made as x.
The other two angles of the triangle are 180 - x (opposite to the extended side) and 180 - (161 - x) (the other two angles on the sides of the triangle).
Since the sum of the exterior angles is 360 degrees, we have:
161 + (180 - x) + (180 - (161 - x)) = 360
Simplifying the equation, we have:
161 + 180 - x + 180 - 161 + x = 360
521 - x + x = 360
521 = 360
This equation is not possible, so there is no solution. Therefore, the value of x cannot be determined.
The correct answer is D. The value of x cannot be determined.