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

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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°