Final Answer:
The measure of ∠Z3 is:
B) 114°
Step-by-step explanation:
In a triangle, the sum of all interior angles is always 180 degrees. ∠Z3 is an exterior angle formed by extending one side of the triangle. By the Exterior Angle Theorem, ∠Z3 is equal to the sum of the two non-adjacent interior angles. Since ∠Z1 and ∠Z2 are given as 63° and 51°, respectively, their sum is 114°. Therefore, ∠Z3 is also 114°.
The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. In this case, ∠Z3 is formed by extending the side opposite ∠Z1 and ∠Z2. So, ∠Z3 = ∠Z1 + ∠Z2. Substituting the given values, ∠Z3 = 63° + 51° = 114°.
This concept is based on the fact that the interior and exterior angles of a triangle are related, and understanding this relationship allows us to determine the measure of an exterior angle using the measures of the interior angles. Therefore, the correct measure of ∠Z3 is 114°, making option B the correct answer.