Question

51° 57° acute triangle right triangle obtuse triangle

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let the third angle be $x$. Then $x+51^{\circ}+57^{\circ}=180^{\circ}$.

Step2: Solve for the third angle

$x = 180^{\circ}-(51^{\circ}+57^{\circ})=180^{\circ}-108^{\circ}=72^{\circ}$.

Step3: Classify the triangle

Since all angles ($51^{\circ}$, $57^{\circ}$, and $72^{\circ}$) are less than 90° (acute angles), the triangle is an acute - triangle.

Answer:

Acute triangle