Question

input: x, an angle
output: y, the angle supplementary to x

input (x) | 10° | 26° | 45° | 90° | 112° | 175°
output (y) | 170° | 154° | | | |

b. is the rule a function? explain.

Explanation:

Step1: Define supplementary angle rule

Supplementary angles sum to $180^\circ$, so $y = 180^\circ - x$.

Step2: Calculate $y$ for $45^\circ$

$y = 180^\circ - 45^\circ = 135^\circ$

Step3: Calculate $y$ for $90^\circ$

$y = 180^\circ - 90^\circ = 90^\circ$

Step4: Calculate $y$ for $112^\circ$

$y = 180^\circ - 112^\circ = 68^\circ$

Step5: Calculate $y$ for $175^\circ$

$y = 180^\circ - 175^\circ = 5^\circ$

Step6: Analyze if it is a function

Each input $x$ has exactly one output $y$.

Answer:

Filled Table:

Input (x)	$10^\circ$	$26^\circ$	$45^\circ$	$90^\circ$	$112^\circ$	$175^\circ$

Part b Answer:

Yes, the rule is a function. Each input angle $x$ corresponds to exactly one output supplementary angle $y$, satisfying the definition of a function (each input has a unique output).