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≠15. the triangles are similar because they each have an interior angle with measure 15°. the triangles are not similar because x≠y. the triangles are similar because y = 130 and there are three pairs of congruent angles.

Explanation:

Step1: Find the value of \(x\)

The sum of interior angles of a triangle is \(180^{\circ}\). For \(\triangle ABC\), we have \(130 + x+15=180\).

$$x = 180-(130 + 15)=35$$

Step2: Find the value of \(y\)

For \(\triangle DEF\), using the sum of interior angles formula \(35+15 + y=180\).

$$y=180-(35 + 15)=130$$

Step3: Check the similarity of triangles

Two triangles are similar if their corresponding angles are equal. In \(\triangle ABC\) the angles are \(130^{\circ},35^{\circ},15^{\circ}\) and in \(\triangle DEF\) the angles are \(130^{\circ},35^{\circ},15^{\circ}\)

Answer:

The triangles are similar because \(y = 130\) and there are three pairs of congruent angles.