Question

think about the process arman is building a bench. the bench comes out from the wall and there is a brace below like in the figure. the angle created between the wall and the brace is 54.9°. what is the equation to solve for the missing angle? what is the measure of the missing angle? which of the following is the correct equation to solve for the missing angle? a. x°+90°+54.9° = 180° b. x°+54.9° = 180° c. x°+100°+54.9° = 180°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the given right - angled triangle (the angle between the wall and the bench is 90°), if one angle is 90° and another is 54.9°, and the missing angle is \(x\).
The equation for the sum of angles is \(x + 90+54.9 = 180\).

Step2: Solve for \(x\)

We can rewrite the equation \(x+90 + 54.9=180\) as \(x=180-(90 + 54.9)\). First, calculate \(90 + 54.9=144.9\). Then \(x = 180-144.9=35.1\).

Answer:

The correct equation to solve for the missing angle is A. \(x^{\circ}+90^{\circ}+54.9^{\circ}=180^{\circ}\), and the measure of the missing angle is \(35.1^{\circ}\).