Question

9/9 triangle angle sum theorem your turn! multiple-choice question what is the measure of the missing angle in question 3? 30 80 180 40

Explanation:

Step1: Recall Triangle Angle Sum Theorem

The sum of the interior angles of a triangle is \(180^\circ\). Let the missing angle be \(x\). The known angles are \(20^\circ\) and \(120^\circ\).

Step2: Set up the equation

Using the theorem, we have \(20^\circ + 120^\circ + x = 180^\circ\).

Step3: Solve for \(x\)

First, calculate \(20^\circ+120^\circ = 140^\circ\). Then, \(x = 180^\circ - 140^\circ = 40^\circ\). Wait, no, wait, let's check again. Wait, the triangle in question 3: looking at the diagram, the angles are \(20^\circ\), \(120^\circ\), and \(x\)? Wait, no, maybe I misread. Wait, no, let's recalculate. Wait, \(180 - 20 - 120 = 40\)? Wait, but the options have 40? Wait, no, wait, maybe the angles are different. Wait, no, the triangle angle sum is 180. So if two angles are 20 and 120, then \(x = 180 - 20 - 120 = 40\). Wait, but let's check the options. The options are 30, 80, 180, 40. So 40 is an option. Wait, but maybe I made a mistake. Wait, no, let's do it again. \(20 + 120 = 140\), \(180 - 140 = 40\). So the missing angle is 40.

Answer:

40 (corresponding to the option with 40, e.g., if the option is D. 40, then D. 40)