Question

find the measure of the numbered angle. m∠6 = □ °

Explanation:

Step1: Find the measure of ∠1

In a right - triangle, the sum of angles is \(180^{\circ}\). For the right - triangle with a \(40^{\circ}\) angle, \(\angle1=180^{\circ}-90^{\circ}-40^{\circ}\)

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Step2: Use the property of vertical angles

Since \(\angle1\) and \(\angle3\) are vertical angles, \(\angle3=\angle1 = 50^{\circ}\)

Step3: Find the measure of ∠5

In the right - triangle (where \(\angle7 = 90^{\circ}\) is part of a linear pair with the right - angle of the triangle), and using the fact that \(\angle3\) and \(\angle5\) are complementary (because the sum of angles in a right - triangle is \(180^{\circ}\) and one angle is \(90^{\circ}\)). \(\angle5=180^{\circ}-90^{\circ}-\angle3\)

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Step4: Use the property of vertical angles again

Since \(\angle5\) and \(\angle8\) are vertical angles.

Answer:

\(40\)