Question

type the correct answer in the box.

in triangle abc, which side is the longest if these are the measures of the angles?

(m\angle a = 60^{\circ}), (m\angle b = 67^{\circ}), (m\angle c = 53^{\circ})

side is the longest side.

Explanation:

Identify the given angle measures

We are given the measures of the three interior angles of \(\triangle ABC\):

$$ m\angle A = 60^\circ,\quad m\angle B = 67^\circ,\quad m\angle C = 53^\circ $$

Compare the angle measures

To find the longest side, we first compare the sizes of the angles:

$$ 67^\circ > 60^\circ > 53^\circ $$

Thus, the largest angle is \(\angle B\).

Apply the angle-side relationship

In any triangle, the longest side is always opposite the largest angle.
The side opposite to vertex \(B\) in \(\triangle ABC\) is side \(AC\).

Determine the longest side

Since \(\angle B\) is the largest angle, the side opposite to it, which is \(AC\), must be the longest side.

Answer:

In triangle ABC, which side is the longest if these are the measures of the angles?
\(m\angle A = 60^\circ\), \(m\angle B = 67^\circ\), \(m\angle C = 53^\circ\)

Side <blank>\(AC\)</blank> is the longest side.