Question

the perimeter of \\( \triangle abc \\) is 300 centimeters.

• \\( ab = 88 \\) centimeters
• \\( bc = 76 \\) centimeters

which statement is true about the interior angles of \\( \triangle abc \\)?
\\( \bigcirc m\angle c \\) is the least of the interior angles
\\( \bigcirc m\angle c \\) is the greatest of the interior angles
\\( \bigcirc m\angle b \\) is the least of the interior angles
\\( \bigcirc m\angle b \\) is the greatest of the interior angles

Explanation:

Step1: Calculate the length of side \(AC\)

The perimeter of \(\triangle ABC\) is \(P = AB+BC + AC\). Given \(P = 100\) cm, \(AB = 80\) cm, and \(BC=76\) cm. Then \(AC=P-(AB + BC)=100-(80 + 76)\). Wait, no, that's wrong. Wait, perimeter formula is correct. Wait, no, \(AB + BC+AC=100\). So \(AC=100-(80 + 76)\) is wrong. Wait, no, \(AB = 18\) cm (assuming a typo, because \(80+76>100\). Let's recalculate. If \(AB = 18\) cm (maybe mis - read), \(BC = 76\) cm, then \(AC=100-(18 + 76)=6\) cm.
In a triangle, the larger side is opposite the larger angle.
We know that \(BC = 76\) cm, \(AB = 18\) cm, \(AC = 6\) cm.
The angle opposite \(AC\) is \(\angle B\), the angle opposite \(AB\) is \(\angle C\), and the angle opposite \(BC\) is \(\angle A\).
Since \(AC

Answer:

\(m\angle B\) is the least of the interior angles.