Question

1. what is the sum of i° + k°?

options: 260°, 140°, 220°, 320°

Explanation:

Step1: Identify full circle angle

A full circle is $360^\circ$. For the angle $i^\circ$, we know $i^\circ + 40^\circ = 360^\circ$.

Step2: Solve for $i^\circ$

Rearrange to find $i^\circ$:
$i^\circ = 360^\circ - 40^\circ = 320^\circ$

Step3: Identify linear pair for $k^\circ$

$k^\circ$ and $40^\circ$ are supplementary (linear pair), so $k^\circ + 40^\circ = 180^\circ$.

Step4: Solve for $k^\circ$

Rearrange to find $k^\circ$:
$k^\circ = 180^\circ - 40^\circ = 140^\circ$

Step5: Calculate the sum

Add $i^\circ$ and $k^\circ$:
$i^\circ + k^\circ = 320^\circ + 140^\circ$

Step1: Reflex angle $i^\circ$ calculation

Reflex $i^\circ = 360^\circ - 40^\circ = 320^\circ$

Step2: $k^\circ$ as supplementary angle

$k^\circ = 180^\circ - 40^\circ = 140^\circ$

Step3: Sum the two angles

$i^\circ + k^\circ = 320^\circ + 140^\circ$

Answer:

$460^\circ$

(Note: If the question intends to reference the reflex angles marked as $i^\circ$ and $k^\circ$: $i^\circ$ is the reflex angle, so $i^\circ = 360^\circ - 40^\circ = 320^\circ$; $k^\circ$ is the reflex angle, so $k^\circ = 360^\circ - (180^\circ - 40^\circ) = 220^\circ$, sum = $320^\circ + 220^\circ = 540^\circ$. But based on standard angle labeling for such problems, the first calculation aligns with the marked angle labels. However, if we consider the answer options provided, the intended sum is $320^\circ + 140^\circ = 460^\circ$, which is derived from the marked $i^\circ$ (reflex) and $k^\circ$ (supplementary to 40°).)

Correction based on answer options: