Question

the sum of the interior angle measures of a triangle must be 180°. so, ( mangle1 + mangle3 + mangle4 = 180^circ ). we are given that ( mangle1 = 37^circ ) and ( mangle4 = 108^circ ). therefore, ( mangle1 + mangle4 = 145^circ ). and so ( mangle3 = 35^circ ). from the figure, we can see that ( mangle2 + mangle3 = 180^circ ). using the value we already found for ( mangle3 ), we find that ( mangle2 = 145^circ ). therefore, ( mangle2 ) (\boldsymbol{=}) ( mangle1 + mangle4 ). this result is an example of the exterior angle property of triangles. for any triangle, the measure of an exterior angle select

Explanation:

Step1: Analyze the given information

We know that \( m\angle1 + m\angle4 = 145^\circ \) (from \( m\angle1 = 37^\circ \) and \( m\angle4 = 108^\circ \), \( 37 + 108 = 145 \)) and also \( m\angle2 + m\angle3 = 180^\circ \) (sum of angles in a triangle's linear pair or straight line) and \( m\angle1 + m\angle3 + m\angle4 = 180^\circ \) (sum of interior angles of a triangle). But we are to find the relationship between \( m\angle2 \) and \( m\angle1 + m\angle4 \). We know \( m\angle1 + m\angle4 = 145^\circ \) and \( m\angle2 = 145^\circ \) (from the figure's angle sum and given values). So we compare \( m\angle2 \) and \( m\angle1 + m\angle4 \).

Step2: Compare the values

Since \( m\angle1 + m\angle4 = 145^\circ \) and \( m\angle2 = 145^\circ \), we can say \( m\angle2 = m\angle1 + m\angle4 \).

Answer:

\( m\angle2 = m\angle1 + m\angle4 \) (so the symbol in the box should be \( = \))