Question

Given triangle ABC~ triangle DEF and m

Answer 1

`\large\boxed{\tt m \angle E = 58^(\circ).}`

Explanation:

`\textsf{We are given 2 triangles that are \underline{similar}, and m} \tt \measuredangle A = 32^(\circ).`

`\textsf{Our goal is to find m} \tt \angle E.`

`\large\underline{\textsf{What are Similar Triangles?}}`

`\textsf{Similar Triangles are 2(+) triangles that have congruent angles, but proportionate}`

`\textsf{side lengths. These triangles are different due to the size of the triangles, the}`

`\textsf{difference is called the \underline{Scale Factor}.}`

`\textsf{*Note that} \ \boxed{\sim} \ \textsf{means that 2 triangles are \underline{similar}.}`

`\large\underline{\textsf{What is Scale Factor?}}`

`\textsf{Scale Factor represents how much larger, or smaller a triangle is with a ratio, or}`

`\textsf{a whole number. For Special Right Triangles, the side length will be multiplied}`

`\textsf{by the Scale Factor.}`

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

`\textsf{Similar Triangles have congruent angles, however we can't assume that}`

`\tt m \angle E \ \textsf{is 32}^(\circ). \textsf{This is due to both angles being in different spots. However though,}`

`\tt \angle D = 32^(\circ). \ m \angle A \ and \ \angle D \ \textsf{are in the same spot, hence they're congruent.}`

`\textsf{Note the symbol shown for} \tt \ \measuredangle C \ and \ \measuredangle F; \ \textsf{this means that they're \underline{Right Angles}.}`

`\textsf{Right Angles are angles that are} \ \tt 90^(\circ). \ \textsf{Because of this, we can form an equation.}`

`\tt m \angle E = 180^(\circ) \ (Sum \ of \ All \ 3 \ Angles) - m \measuredangle A - m \measuredangle C.`

`\underline{\textsf{After Substituting;}}`

`\tt m \angle E = 180^(\circ) - 32^(\circ) - 90^(\circ).`

`\underline{\textsf{Evaluating;}}`

`\large\boxed{\tt m \angle E = 58^(\circ).}`