Sure, let's solve this step-by-step.
1. Understanding Complementary Angles:
Complementary angles are two angles that sum up to 90 degrees. Thus, if angle ZA and angle B are complementary, their measures will add up to 90 degrees.
2. Define Variables:
Let's say the measure of angle ZA is [tex]\( x \)[/tex] degrees. According to the problem, the measure of angle B (denoted as [tex]\( m(B) \)[/tex]) is 14 degrees more than the measure of angle ZA.
3. Set Up the Equation:
Since angle B is 14 degrees more than angle ZA, we can express the measure of angle B as:
[tex]\[
m(B) = x + 14
\][/tex]
4. Write the Complementary Angle Condition:
Since ZA and B are complementary, their sum is 90 degrees:
[tex]\[
x + (x + 14) = 90
\][/tex]
5. Solve the Equation:
Combine like terms:
[tex]\[
2x + 14 = 90
\][/tex]
Isolate [tex]\( x \)[/tex]:
[tex]\[
2x = 90 - 14
\][/tex]
[tex]\[
2x = 76
\][/tex]
[tex]\[
x = \frac{76}{2}
\][/tex]
[tex]\[
x = 38
\][/tex]
So, the measure of angle ZA is [tex]\( 38 \)[/tex] degrees.
6. Find the Measure of Angle B:
Since [tex]\( m(B) \)[/tex] is 14 degrees more than the measure of angle ZA:
[tex]\[
m(B) = 38 + 14 = 52
\][/tex]
7. Conclusion:
Therefore, the measure of angle ZA is [tex]\( 38 \)[/tex] degrees and the measure of angle B is [tex]\( 52 \)[/tex] degrees.
These angles sum to:
[tex]\[
38 + 52 = 90 \text{ degrees}
\][/tex]
Thus, the solution is verified.
