Question

find ( mangle 1 ). then classify the triangle by its angles.
( mangle 1 = square^circ ).
the triangle can be classified by its angles as
right
obtuse
equiangular
acute

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). Let \(m\angle1 = x\). We know two angles: \(30^\circ\) and \(40^\circ\). So, \(x + 30 + 40 = 180\).

Step2: Solve for \(x\)

Simplify the left side: \(x + 70 = 180\). Subtract \(70\) from both sides: \(x = 180 - 70 = 110\).

Step3: Classify the triangle

An obtuse triangle has one angle greater than \(90^\circ\). Since \(110^\circ>90^\circ\), the triangle is obtuse.

Answer:

\(m\angle1 = \boldsymbol{110}^\circ\).
The triangle can be classified by its angles as \(\boldsymbol{\text{obtuse}}\).