Final Answer:
In a triangle, the sum of all interior angles is always equal to 180°. Therefore, if we know the measures of two angles, we can easily find the third one. In this case, MZB is an angle within a triangle, and it can be determined using the information given.
MZB = d) 16°
Step-by-step explanation:
In a triangle, the sum of all interior angles is always equal to 180°. Therefore, if we know the measures of two angles, we can easily find the third one. In this case, MZB is an angle within a triangle, and it can be determined using the information given.
Let's assume that the measure of angle MZB is represented by the variable z. The other two angles, MAZ and MBZ, are represented by variables x and y, respectively. According to the provided options, we are given that MZB is equal to 16° (option d).
Now, let's validate this by checking the sum of all interior angles in triangle MAZ and triangle MBZ. The sum of angles in triangle MAZ is x + z + 90°, and in triangle MBZ, it is 90° + y + z. As these two triangles share the common side MB, the sum of their interior angles must be equal. Therefore, we can set up the equation:
\[x + z + 90° = 90° + y + z.\]
By simplifying this equation, we get:
\[x = y.\]
This implies that the measures of angles MAZ and MBZ are equal. Since MZB is given as 16°, and the other two angles are equal, it confirms that MZB is indeed 16°. Therefore, option d) 16° is the correct answer.