Question

△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 .

Answer 1

it is y=130 because they are congruent

Answer 2

(C)

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.