A side of the triangle below has been
extended to for an exterior angle of
161°. Find the value of x. (The other angle is 46)
To find the value of x, we need to use the fact that the sum of the measures of the exterior angles of any triangle is always 360°.
Let's call the side that has been extended x.
The given exterior angle is 161°.
The other angle of the triangle is 46°.
To find the measure of the third angle, we subtract the sum of the other two angles from 360°:
Third angle = 360° - 161° - 46°
Third angle = 153°
Now we can set up an equation with the third angle and the given angle to find the value of x:
x + 46° + 153° = 180°
x + 199° = 180°
Subtracting 199° from both sides, we get:
x = 180° - 199°
x = -19°
Therefore, the value of x is -19°.