Question

find the measure of the numbered angle.
m/3 = □

Explanation:

Step1: Find the measure of the third angle in the top - right triangle

In a right - triangle, the sum of angles is \(180^{\circ}\). Given one angle is \(40^{\circ}\) and another is \(90^{\circ}\). Let the third angle be \(x\). Then \(x + 40^{\circ}+90^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-(40^{\circ}+90^{\circ})=50^{\circ}\). This angle \(x\) is equal to \(\angle1\) (vertical angles are equal). So \(m\angle1 = 50^{\circ}\).

Step2: Use the property of supplementary angles

Since \(\angle1\) and \(\angle2\) are supplementary (they form a linear pair), \(m\angle1+m\angle2 = 180^{\circ}\). Substitute \(m\angle1 = 50^{\circ}\) into the equation: \(50^{\circ}+m\angle2=180^{\circ}\).

Step3: Solve for \(m\angle2\)

Subtract \(50^{\circ}\) from both sides of the equation \(50^{\circ}+m\angle2 = 180^{\circ}\). We get \(m\angle2=180^{\circ}-50^{\circ}=130^{\circ}\).

Answer:

\(130\)