To determine the measure of angle [tex]\(B\)[/tex] given that angles [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are complementary, and the measure of angle [tex]\(A\)[/tex] is [tex]\(y^\circ\)[/tex], follow these steps:
1. Understand the Definition of Complementary Angles:
Two angles are complementary if the sum of their measures is [tex]\(90^\circ\)[/tex].
2. Set Up the Equation:
Since angles [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are complementary, we have:
[tex]\[
A + B = 90^\circ
\][/tex]
3. Substitute the Measure of Angle [tex]\(A\)[/tex]:
We know that the measure of angle [tex]\(A\)[/tex] is [tex]\(y^\circ\)[/tex].
Thus, the equation becomes:
[tex]\[
y + B = 90^\circ
\][/tex]
4. Solve for Angle [tex]\(B\)[/tex]:
To find [tex]\(B\)[/tex], isolate [tex]\(B\)[/tex] on one side of the equation:
[tex]\[
B = 90^\circ - y
\][/tex]
So, the measure of angle [tex]\(B\)[/tex] is [tex]\((90 - y)^\circ\)[/tex].
Therefore, the correct answer is:
[tex]\[
(90 - y)^\circ
\][/tex]
