Question

5/13
what steps would you take to solve for y?
find the number of sides, find the sum of the interior angles, then subtract from that
subtract from 360
subtract from 180
divide 360 by the number of sides

Explanation:

Step1: Identify the problem type

This is a problem about finding an unknown angle (y) in a geometric figure, likely involving the sum of exterior angles or interior angles of a polygon. The key is to use the fact that the sum of exterior angles of any polygon is \( 360^\circ \), or the sum of interior angles is \( (n - 2)\times180^\circ \) where \( n \) is the number of sides. But first, we need to find the sum of the given angles and subtract from \( 360^\circ \) (if exterior angles) or use the interior angle sum formula. Wait, looking at the figure, it seems to be about exterior angles or a triangle - related? Wait, the options include "subtract from 360" and "find the number of sides, find the sum of the interior angles, then subtract from that" etc. Wait, first, let's recall: for a polygon, the sum of exterior angles is \( 360^\circ \). So if we have some exterior angles (or angles related to the polygon's angles), we can sum the known angles and subtract from \( 360^\circ \) to find the unknown. Wait, the steps: first, find the sum of the given angles (70°, 60°, 65°, 40° and y? Wait, no, the figure has angles 70°, 60°, 65°, 40°, and we need to find y. Wait, maybe it's a polygon (like a quadrilateral? No, the figure looks like a triangle with some exterior angles? Wait, no, the sum of exterior angles of any polygon is 360°. So first, sum the known angles: 70 + 60 + 65 + 40 = let's calculate: 70 + 60 = 130, 130 + 65 = 195, 195 + 40 = 235. Then subtract from 360: 360 - 235 = 125? Wait, but the steps: the correct step would be to sum the known angles and subtract from 360. Wait, the options: one of them is "subtract from 360" (maybe the step is: sum the given angles, then subtract from 360 to get y). Wait, the question is "What steps would you take to solve for y?" So the steps: first, find the sum of the given angles (70°, 60°, 65°, 40°), then subtract that sum from 360° (since the sum of exterior angles of any polygon is 360°). Wait, let's check the options. The options are:

1. subtract from 360

2. find the number of sides, find the sum of the interior angles, then subtract from that

3. subtract from 180

4. divide 360 by the number of sides

Wait, the correct approach for exterior angles: sum the known angles, subtract from 360. So the step is: sum the given angles (70 + 60 + 65 + 40 = 235), then subtract from 360: 360 - 235 = 125. So the step is to subtract the sum of the known angles from 360. So the correct step is "subtract from 360" (after summing the known angles). Wait, but the options: the first option is "subtract from 360" (maybe the step is: sum the existing angles, then subtract from 360 to get y). So the steps: first, calculate the sum of the given angles (70° + 60° + 65° + 40° = 235°), then subtract this sum from 360° (since the sum of exterior angles of any polygon is 360°) to find y. So the step is "subtract from 360" (after summing the known angles). So the correct step is to sum the known angles and then subtract from 360. So the answer would be the option that says "subtract from 360" (but wait, the options are:

- subtract from 360

- find the number of sides, find the sum of the interior angles, then subtract from that

- subtract from 180

- divide 360 by the number of sides

So the correct step is to sum the given angles (70, 60, 65, 40) and subtract from 360 to get y. So the step is "subtract from 360" (after summing the known angles). So the answer is the option "subtract from 360".

Wait, but let's confirm. The sum of exterior angles of any convex polygon is 360 degrees. So if we have a polygon (maybe a pentagon? No, the angles given are 70, 60, 65, 40, and y. So that's five angles? Wait, no, the figure: maybe it's a quadrilateral? No, the angles: 70, 60, 65, 40, and y. Wait, maybe it's a triangle with some exterior angles? No, the sum of exterior angles of a triangle is also 360? Wait, no, the sum of exterior angles of any polygon (convex) is 360 degrees, regardless of the number of sides. So regardless of the number of sides, the sum of exterior angles is 360. So if we have several exterior angles (or angles that are equivalent to exterior angles), we can sum them and subtract from 360 to find the missing one. So the steps: sum the known angles (70 + 60 + 65 + 40 = 235), then subtract from 360: 360 - 235 = 125. So the step is to subtract the sum of the known angles from 360. So the correct option is "subtract from 360".

Answer:

The step is to sum the given angles (70°, 60°, 65°, 40°) and then subtract that sum from 360° to find y. So the correct option (from the given choices, assuming one of them is "subtract from 360") is the one that says "subtract from 360".