Question

writing for the figure shown, find m∠1. use pencil and paper. explain two ways to find the missing angle measure of the triangle. m∠1=□°

Explanation:

Step1: Use the triangle - angle sum property

The sum of angles in a triangle is \(180^{\circ}\). In the right - angled triangle (one angle is \(90^{\circ}\)), let the third angle (other than \(33^{\circ}\) and \(90^{\circ}\)) be \(x\). Then \(x + 33^{\circ}+90^{\circ}=180^{\circ}\). Solving for \(x\):

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Since \(\angle1\) and \(x\) are supplementary (form a linear pair, sum to \(180^{\circ}\)), \(\angle1=180^{\circ}-x\). Substituting \(x = 57^{\circ}\), \(\angle1=180^{\circ}-57^{\circ}=123^{\circ}\)

Step2: Use the exterior - angle property

The exterior - angle property of a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
In the given triangle, the exterior angle \(\angle1\) is equal to the sum of the two non - adjacent interior angles (\(33^{\circ}\) and \(90^{\circ}\)). So, \(\angle1=33^{\circ}+90^{\circ}\)

Answer:

\(123\)