Decide whether the statement is always, sometimes, or never true. The measure of an exterior angle of a triangle is greater than the sum of the measures of the two opposite interior angles.
Draw a simple triangle. Label the interior angles x, y, and z. Draw the exterior angle for the angle marked z, and call it z'. Now, consider what you know about a triangle: all interior angles must add up to 180 degrees. Therefore: \[x+y+z=180\]Also, since the angle z' is exterior to angle z, z' and z must be supplementary (add up to 180 degrees): \[z'+z=180\]Since both statements are true, solve the second one for z, substitute your results into the original equation, and see what the relationship is between x, y, and z'.
...so always sometimes or never? i have to solve this quick. =\
\[z=180-z'\]\[x+y+(180-z')=180\]\[x+y-z'=0\]\[x+y=z'\]\[z'=x+y\]In other words, the exterior angle is equal to the sum of the two interior opposite angles.
Join our real-time social learning platform and learn together with your friends!