Question

solve for ( mangle uvx ) if ( mangle uvw = 82^{circ} ) and ( mangle xvw = 40^{circ} ).

Explanation:

Step1: Use angle - subtraction formula

We know that \(m\angle UVW=m\angle UVX + m\angle XVW\) (angle - addition postulate). So, to find \(m\angle UVX\), we can rewrite the formula as \(m\angle UVX=m\angle UVW - m\angle XVW\).

Step2: Substitute the given values

Given \(m\angle UVW = 82^{\circ}\) and \(m\angle XVW=40^{\circ}\). Substitute these values into the formula: \(m\angle UVX = 82^{\circ}-40^{\circ}\).

Step3: Calculate the result

\(82 - 40=42\), so \(m\angle UVX = 42^{\circ}\).

Answer:

\(42^{\circ}\)