Question

Solve for y
A)115º
B)108º
C)90º
D)130º

Answer 1

`\large\boxed{\tt y = 115^(\circ).}`

Explanation:

`\textsf{We are asked to find the measure of} \ \tt \angle Y.`

`\textsf{We are given a shape, but we aren't given what shape it is.}`

`\large\underline{\textsf{What is a Shape?}}`

`\textsf{A Shape is a specific outline sometimes dependent of how many sides it has.}`

`\underline{\textsf{Shapes that depend on outlines;}}`

• 
  `\textsf{Non-Polygons,}`
• 
  `\textsf{Shapes that aren't quadrilaterals,}`
• 
  `\textsf{Any shapes that are not classified under something.}`

`\underline{\textsf{Shapes that depend on the number of sides;}}`

`\textsf{Mainly the opposite.}`

• 
  `\textsf{Polygons,}`
• 
  `\textsf{Quadrilaterals,}`
• 
  `\textsf{Any shapes that are classified under something.}`

`\textsf{Because our shape has 5 sides, it's dependent on the amount of sides it has, which}`

`\textsf{makes the shape a Polygon.}`

`\large\underline{\textsf{What is a Polygon?}}`

`\textsf{A Polygon is a closed shape that classifies as a;}`

• 
  `\textsf{Triangle, or any shape with 3 sides,}`
• 
  `\textsf{Square/Rectangle, or any shape with 4 sides,}`
• 
  `\textsf{Pentagon, or any shape with 5 sides,}`
• 
  `\textsf{Hexagon, or any shape with 6 sides,}`
• 
  `\textsf{Heptagon, or any shape with 7 sides,}`
• 
  `\textsf{Octagon, or any shape with 8 sides,}`
• 
  `\textsf{Nonagon, or any shape with 9 sides,}`
• 
  `\textsf{Decagon, or any shape with 10 sides.}`

`\textsf{The list goes on forever.}`

`\textsf{Our shape is a Pentagon, due to the shape having 5 sides.}`

`\large\underline{\textsf{What is a Pentagon made up of?}}`

`\textsf{A Pentagon is a polygon that has 5 sides, meaning that it has 5 angles.}`

`\textsf{The total of the angles is what we should find out with a pattern.}`

`\underline{\textsf{What is the total of all the angles' measures of a Pentagon?}}`

`\textsf{A Triangle has 3 sides with 3 angles, which add up to 180}^(\circ).`

`\textsf{A Quadrilateral has 4 sides with 4 angles, which add up to 360}^(\circ).`

`\textsf{The Pattern is that when an extra side is added, the total measure of the angles}`

`\textsf{increase by 180}^(\circ).`

`\textsf{A Pentagon has 5 sides with 5 angles, which add up to} \ \boxed{\tt 540^(\circ).}`

`\textsf{Now that we know the total, we can form an equation.}`

`\tt 540^(\circ) = 135^(\circ) + 112^(\circ) + 88^(\circ) + y^(\circ) + 90^(\circ)`

`\textsf{Remember that Right Angles are 90}^(\circ) \ \textsf{angles that are represented with a box}`

`\textsf{symbol.}`

`\large\underline{\textsf{Solving;}}`

`\textsf{Now that we have our equation, we should \underline{combine like terms}, then use the}`

`\textsf{\underline{subtraction rule of equality} to find the measure of y.}`

`\underline{\textsf{Combine Like Terms;}}`

`\tt 540^(\circ) = \boxed{135^(\circ)} + \boxed{112^(\circ)} + \boxed{88^(\circ)} + y^(\circ) + \boxed{90^(\circ)}`

`\tt 540^(\circ) = 425^(\circ) + y^(\circ)`

`\underline{\textsf{Use the Subtraction Rule of Equality;}}`

`\tt 540^(\circ) - 425^(\circ) = 425^(\circ) - 425^(\circ)+ y^(\circ)`

`\large\boxed{\tt y = 115^(\circ).}`