Question

4 - 2 angles of triangles practice
find the measure of the numbered angle.
85°
75°
105°
95°

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(A = 40^{\circ}\), \(B=55^{\circ}\), and \(C=\angle1\). Then, according to the formula \(A + B + C=180^{\circ}\).

Step2: Solve for \(\angle1\)

Substitute \(A = 40^{\circ}\) and \(B = 55^{\circ}\) into the equation \(A + B + C=180^{\circ}\). We get \(C=\angle1=180^{\circ}-(40^{\circ}+55^{\circ})\). First, calculate \(40^{\circ}+55^{\circ}=95^{\circ}\). Then, \(180^{\circ}-95^{\circ}=85^{\circ}\).

Answer:

\(85^{\circ}\)