△abc has interior angles with measures x°, 90°, and 65°, and △def has interior angles with measures y°, 65°, and 20°. using the given information, which statement is true? a the two triangles are not similar because x≠20 and there cannot be three congruent interior angels. b the triangles are similar because they each have an interior angle with measure 65°. c the two triangles are similar because y=90 . d the two triangles are not similar because the interior angles are congruent but the side lengths are different.

A. The two triangles are not similar because x≠20 and there cannot be three congruent interior angels.

Step-by-step explanation:

Given: △ABC has interior angles with measures x°, 90°, and 65°

△DEF has interior angles with measures y°, 65°, and 20°.

If △ABC is similar to △DEF then their corresponding angles should be equal.

Suppose △ABC is similar to △DEF then x=20°

But in △ABC

x+90°+65°=180° [angle sum property of triangle]

⇒x+155°=180°

⇒x=180°-155°

⇒x=25°

⇒x≠20°

⇒△ABC is not similar to △DEF.

Therefore A is the right option.

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step-by-step explanation:

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