Question

for the figure shown, find ( mangle1 ) and ( mangle2 ).
( mangle1=square^{circ} )

Explanation:

Step1: Use the exterior angle property of a triangle

The exterior angle property states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the triangle where \(\angle1\) is an exterior angle, \(\angle1 = 26^{\circ}\) (given non - adjacent interior angle).

Step2: Calculate \(m\angle2\)

First, find the third angle of the larger triangle. Let's call the right - angled triangle's third angle (adjacent to \(\angle2\)) \(x\). In the right - angled triangle (\(90^{\circ}\) angle), using the angle - sum property of a triangle (\(180^{\circ}\) in a triangle), \(x=180^{\circ}-90^{\circ}-27^{\circ}=63^{\circ}\).

Now, consider the straight - line (sum of angles on a straight line is \(180^{\circ}\)). For the angles related to \(\angle2\), we know that \(\angle2 + 26^{\circ}+63^{\circ}=180^{\circ}\) (sum of angles on a straight line). Then \(\angle2=180^{\circ}-(26^{\circ}+63^{\circ})\).

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Answer:

\(m\angle1 = 26^{\circ}\), \(m\angle2=91^{\circ}\)