Question 1

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

Question 2

Answer:

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

Explanation:

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

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

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

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

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

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

$\textsf{Mainly the opposite.}$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$\textsf{symbol.}$

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

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

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

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

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

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

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

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

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

Please log in or register to add a comment.

Please log in or register to answer this question.