Question

Triangle ABC

has interior angles that measure x°, 58°, and 70° .

Triangle DEF has interior angles that measure y°, 70°, and 49°.

Using this information, which statement is true?


The triangles are similar because they each have an interior angle with measure 70°.


The two triangles are similar because 70+58+x=180 means x =50° and 70+49+y=180 means y = 50°


The two triangles are not similar because 70+58+x=180 means x =52° and 70+49+y=180 means y = 61°


The two triangles are similar because y = 90°.

Answer 1

`▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪`

Let's solve for value of values of x and y ~

According to Angle sum property of triangles :

`\qquad \sf  \dashrightarrow \: 70 \degree + 58\degree + x = 180\degree`

`\qquad \sf  \dashrightarrow \: x\degree + 128\degree = 180\degree`

`\qquad \sf  \dashrightarrow \:x = 180\degree - 128\degree`

`\qquad \sf  \dashrightarrow \: x = 52\degree`

Now, solve for y ~

`\qquad \sf  \dashrightarrow \: 70\degree + 49\degree + y = 180\degree`

`\qquad \sf  \dashrightarrow \: y + 119 = 180\degree`

`\qquad \sf  \dashrightarrow \: y = 180 - 119\degree`

`\qquad \sf  \dashrightarrow \: y = 61 \degree`

Now, by the results we got, we can conclude that :

The two triangles are not similar because 70 + 58 + x = 180 means x = 52° and 70 + 49 + y=180 means y = 61°

Answer 2

» Let's solve for value of values of x and y

⛥Solve for
`x` :

`⟿70° +58° + x = 180°`

`⟿x + 128° = 180°`

`⟿x = 180° - 128°`

`⟿x = 52°`

⛥Solve for
`y` :

`⟿70° +49° + y = 180°`

`⟿y+119 = 180°`

`⟿y = 180 - 119°`

`⟿y = 61°`

The two triangles are not similar because

70 +58 + x = 180 means x = 52°

70 + 49 + y = 180° means y = 61°