Answer:
z = 134°
Explanation:
You want to know the measure of exterior angle z given remote interior angles of the triangle are 77° and 57°.
Exterior angle
The exterior angle of a triangle is equal to the sum of the remote interior angles of the triangle. (It is useful to remember this.)
z = 77° +57°
z = 134°
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Additional comment
As you know the value of the interior angle at C will be the supplement of the value of z: (180° -z). Then the sum of the interior angles is ...
77° +57° +(180°-z) = 180°
Add (z -180°) to both sides of this equation and you get ...
77° +57° +(180°-z) +(z -180°) = 180° +(z -180°)
77° +57° = z . . . . simplified