Question

for the figure shown, find ( mangle1 ) and ( mangle2 ).
( mangle1=square^{circ} )
(the figure is not drawn to scale)

Explanation:

Step1: Use the exterior angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the smaller triangle, if we consider the angle with measure \(31^{\circ}\) and \(\angle1\), we know that the exterior angle (let's assume it's related to the angle formed with the \(97^{\circ}\) angle) is not directly used here. But if we consider the property of angles in a triangle - like the fact that \(\angle1\) and \(31^{\circ}\) and the angle adjacent to \(97^{\circ}\) (let's call it \(x\)) form a triangle. However, a more straightforward way: if we assume that \(\angle1\) and \(31^{\circ}\) are related to the \(97^{\circ}\) angle. Wait, no, using the exterior angle property for the triangle where one non - adjacent interior angle is \(31^{\circ}\) and \(\angle1\) and the exterior angle is \(97^{\circ}-36^{\circ}\) (wait no, wrong approach). Wait, actually, if we consider that \(\angle1\) and \(31^{\circ}\) are such that if we assume a straight line or some other relation. Wait, no, using the exterior angle property of a triangle: \(\angle1+31^{\circ}=97^{\circ}\) (assuming that the side with \(\angle1\) and \(31^{\circ}\) forms a triangle where \(97^{\circ}\) is an exterior angle).

$$ \angle1=97^{\circ}-31^{\circ} $$

Step2: Calculate \(\angle1\)

$$ \angle1 = 66^{\circ} $$

Answer:

\(66\)