Question

1. ( mangle deb = x + 44 ), ( mangle def = 76^circ ), and ( mangle bef = x + 50 ). find ( x ).

Explanation:

Step1: Use angle addition postulate

From the diagram, we know that \( m\angle DEF = m\angle DEB + m\angle BEF \). Substituting the given angle measures, we get \( 76=(x + 44)+(x + 50) \).

Step2: Simplify the equation

First, combine like terms on the right - hand side: \( 76=2x+94 \). Then, subtract 94 from both sides of the equation: \( 76 - 94=2x+94 - 94 \), which simplifies to \( - 18 = 2x \).

Step3: Solve for x

Divide both sides of the equation \( -18 = 2x \) by 2: \( x=\frac{-18}{2}=-9 \).

Answer:

\( x=-9 \)