Question

directions: use the angle addition postulate to answer each questions. show all work.

1. ( mangle qrt = 132^{circ} ). find ( x ).
2. ( mangle abd + mangle abc = 228^{circ} ). find ( x ).
3. ( mangle efg + mangle gfh = 221^{circ} ). find ( x ).
4. ( mangle hij + mangle jik = 198^{circ} ). find ( x ).
5. ( mangle tuw = 105^{circ} ). find ( mangle tuv ).
6. ( mangle abd = 122^{circ} ). find ( mangle cbd ).

Explanation:

Step1: Apply Angle Addition Postulate

According to the Angle Addition Postulate, \(m\angle QRT=m\angle QRS + m\angle SRT\). Given \(m\angle QRT = 132^{\circ}\), \(m\angle QRS=(5x)^{\circ}\), and \(m\angle SRT=(6x)^{\circ}\), we have the equation \(5x + 6x=132\).

Step2: Solve the Equation

Combine like - terms: \(11x = 132\). Then divide both sides by 11: \(x=\frac{132}{11}\).

Answer:

\(x = 12\)