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جامعة الدوحة للعلوم والتكنولوجيا
UNIVERSITY OF DOHA FOR SCIENCE & TECHNOLOGY

Topic 13: Geometry

121. If ∠P and ∠Q are supplementary angles and ∠P = 12°, what is the measure of ∠Q?

A) 12°
B) 78°
C) 168°
D) 180°
E) None of the above

Sagot :

GinnyAnswer
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°
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