Question

solve for a.
25°
55° a
30°
a = ?°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(x\). So, \(x+25^{\circ}+30^{\circ}=180^{\circ}\).

Step2: Solve for the third - interior angle \(x\)

\(x = 180^{\circ}-(25^{\circ}+30^{\circ})=180^{\circ}-55^{\circ}=125^{\circ}\).

Step3: Use the linear - pair property

The angle \(a\) and the angle \(x\) form a linear pair. Since the sum of angles in a linear pair is 180°, and \(x = 125^{\circ}\), then \(a+125^{\circ}=180^{\circ}\).

Step4: Solve for \(a\)

\(a=180^{\circ}-125^{\circ}=55^{\circ}\).

Answer:

\(55\)