Question

Angle x and angle y are complementary. angle x is supplementary to a 128 angle.What are the measures of angle x and angle y?

Answer 1

`\boxed{\mathtt{x=52^(\circ)}}`

`\boxed{\mathtt{y=38^(\circ)}}`

Explanation:

`\textsf{We are asked to solve for the measures of angles x and y.}`

`\textsf{First, x is supplementary to an angle that equals 128}^(\circ).`

`\Large\underline{\textsf{What are Supplementary Angles?}}`

`\textsf{Supplementary angles are 2 or more angles that add up to \underline{180}}^(\circ).`

`\large\underline{\textsf{This means that;}}`

`\mathtt{x+128^(\circ)=180^(\circ).}`

`\large\underline{\textsf{Subtract 128 from both sides for x:}}`

`\boxed{\mathtt{x=52^(\circ)}}`

`\Large\underline{\textsf{What are Complementary Angles?}}`

`\textsf{Complementary angles are 2 or more angles that add up to \underline{90}}^(\circ).`

`\large\underline{\textsf{This means that;}}`

`\mathtt{x+y=90^(\circ).}`

`\textsf{Because we know x, we can solve for y.}`

`\large\underline{\textsf{Substitute:}}`

`\mathtt{52^(\circ)+y=90^(\circ).}`

`\large\underline{\textsf{Subtract 52 from both sides for y:}}`

`\boxed{\mathtt{y=38^(\circ)}}`

Answer 2

y = 38°

Explanation:

If Angle x and angle y are complementary, then x + y = 90°

Also, if angle x is supplementary to a 128 angle, then x + 128° = 180°.

Solving the latter equation for x, we get x = 52°.

Therefore, by the first equation, x + y = 90° becomes 52° + y = 90°, yielding

y = 38°