Question

the third angle (a3) of a triangle is given by the formula: a3 = 180 - a1 - a2 where we know the first angle (a1) and second angle (a2) of the triangle. which expression completes the calculation for the third angle of a triangle? 180 + angle1 + angle2 180 - angle1 + angle2 180 - angle1 - angle2

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a triangle is 180 degrees. If the three angles are \(a_1\), \(a_2\) and \(a_3\), then \(a_1 + a_2+a_3=180\).

Step2: Solve for \(a_3\)

Isolate \(a_3\) by subtracting \(a_1\) and \(a_2\) from both sides of the equation \(a_1 + a_2+a_3 = 180\). We get \(a_3=180 - a_1 - a_2\).

Answer:

180 - angle1 - angle2