Question

enter the given angle measure
given:
aw bisects ∠cad.
m∠caw = 20°.
enter the measures and reaso
needed to calculate m∠dax
m∠dax =
diagram notes:

Explanation:

Step1: Use the angle - bisector property

Since \(AW\) bisects \(\angle CAD\), then \(m\angle CAD=2\times m\angle CAW\). Given \(m\angle CAW = 20^{\circ}\), so \(m\angle CAD=2\times20^{\circ}=40^{\circ}\).

Step2: Use the angle - addition postulate

We know that \(\angle CAD+\angle DAX+\angle LAX = 180^{\circ}\) (a straight - line angle). But if we assume the relevant relationship from the diagram (assuming \(\angle LAX\) is not part of the non - used angles in the simple calculation based on the given bisected angle and the straight - line concept). A straight - line has an angle measure of \(180^{\circ}\). If we consider the relationship for \(\angle CAD\) and \(\angle DAX\) (assuming the other angles in the diagram that are not related to the bisected angle and the required \(\angle DAX\) are either part of the bisected angle or can be ignored in the basic calculation). We know that \(\angle CAD + \angle DAX=180^{\circ}\) (if we assume the non - bisected part of the straight - line). Since \(m\angle CAD = 40^{\circ}\), then \(m\angle DAX=180^{\circ}-m\angle CAD\).
Substitute \(m\angle CAD = 40^{\circ}\) into the formula: \(m\angle DAX=180 - 40\).

Answer:

\(140\)