Answer: [tex]\large\boxed{\text{B. Complementary}}[/tex]
Step-by-step explanation:
Given information
[tex]\angle A=52^\circ[/tex]
[tex]\angle B=38^\circ[/tex]
Given answer choices
[tex]\text{A. Congruent: means that the two angles have equal measurements}[/tex]
[tex]\text{B. Complementary: means that the angles add up to 90}^\circ[/tex]
[tex]\text{C. Supplementary: means that the angles add up to 180}^\circ[/tex]
[tex]\text{D. Vertical: are formed when two lines intersect each other at a point, which }[/tex]
[tex]\text{means the two angles are equal in measurement.}[/tex]
Eliminate choices A and D
[tex]\text{The two angles }\angle A \text{ and }\angle B \text{ are not equal in measurement}[/tex]
[tex]\text{Therefore, they are neither congruent nor vertical}[/tex]
Add the two angles up
[tex]\angle A+\angle B=(52)+(38)=90^\circ[/tex]
Conclusion
[tex]\text{As given in the answer choice, complementary angles add up to 90}^\circ[/tex]
[tex]\text{Therefore, }\angle A \text{ and } \angle B \text{ are }\large\boxed{\text{Complementary}}[/tex]
Hope this helps!! :)
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