Question

find ( mangle1 ). then classify the triangle by its angles.( mangle1=square^{circ} ).the triangle can be classified by its angles as

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(A = 60^{\circ}\), \(B=60^{\circ}\), and \(C = m\angle1\). Then \(A + B + C=180^{\circ}\).
Substitute \(A = 60^{\circ}\) and \(B = 60^{\circ}\) into the formula: \(60^{\circ}+60^{\circ}+m\angle1 = 180^{\circ}\).

Step2: Solve for \(m\angle1\)

Simplify the left - hand side of the equation: \(120^{\circ}+m\angle1=180^{\circ}\).
Subtract \(120^{\circ}\) from both sides: \(m\angle1=180^{\circ}-120^{\circ}\).
So, \(m\angle1 = 60^{\circ}\).

Step3: Classify the triangle by its angles

Since all three angles (\(60^{\circ},60^{\circ},60^{\circ}\)) are less than \(90^{\circ}\) (acute angles), and all angles are equal.

Answer:

\(m\angle1 = 60^{\circ}\).
The triangle can be classified by its angles as an equiangular (or acute) triangle.