Angles [tex]A[/tex] and [tex]B[/tex] are complementary. The measure of angle [tex]A[/tex] is [tex]y^{\circ}[/tex]. What is the measure of angle [tex]B[/tex]?

A. [tex](180-y)^{\circ}[/tex]
B. [tex](y-90)^{\circ}[/tex]
C. [tex](180+y)^{\circ}[/tex]
D. [tex](90-y)^{\circ}[/tex]



Answer :

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]