△ABC has interior angles with measures 130°, x°, and 15°, and △DEF has interior angles with measures 35°, 15°, and y°. Using the
given information, which statement is true? The triangles are not similar because x≠y . The triangles are similar because they each have an interior angle with measure 15°. The triangles are similar because y=130 and there are three pairs of congruent angles. The triangles are not similar because x≠15 .
2 answers:
Answer:
(C)
Step-by-step explanation:
It is given that △ABC has interior angles with measures 130°, x°, and 15°, and △DEF has interior angles with measures 35°, 15°, and y°.
Using the angle sum property in ΔABC, we have
∠A+∠B+∠C=180°
⇒130°+x+15°=180°
⇒x=180-145
⇒x=35°
Again applying Angle sum property in ΔDEF, we have
∠D+∠E+∠F=180°
⇒35°+15°+y=180°
⇒y=180-50
⇒y=130°
Thus, ∠A=∠F=130°, ∠B=∠D=35° and ∠C=∠E=15°.
Therefore, the two given triangles are similar because y=130° and there are three pairs of congruent angles.
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