To determine the measure of angle ZQ when ZP and ZQ are supplementary angles and ZP is given as 12°, we need to follow these steps:
1. Understand what supplementary angles are:
Supplementary angles are two angles whose measures add up to 180°. This means if you know the measure of one angle, you can always find the measure of the other by subtracting the known angle from 180°.
2. Note the given information:
We are given that angle ZP is 12°.
3. Set up the relationship for supplementary angles:
Since ZP and ZQ are supplementary, we can write the equation:
[tex]\[ \text{ZP} + \text{ZQ} = 180° \][/tex]
4. Substitute the given value:
We know that ZP is 12°, so we substitute 12° for ZP in the equation:
[tex]\[ 12° + \text{ZQ} = 180° \][/tex]
5. Solve for ZQ:
To find the measure of ZQ, subtract 12° from 180°:
[tex]\[ \text{ZQ} = 180° - 12° \][/tex]
[tex]\[ \text{ZQ} = 168° \][/tex]
Thus, the measure of angle ZQ is [tex]\[ 168° \][/tex].
Therefore, the correct answer is:
C) 168°
