Answer:
The measure of [tex]\angle ACD = 42[/tex]
Step-by-step explanation:
Given:
[tex]\angle WZX = 82\\\angle BDC = 56\\[/tex]
construction :
Saul draws a line parallel to [tex]\vec {AB}[/tex]that intersects [tex]\vec {ZA}[/tex] at C and [tex]\vec {ZB}[/tex] at D.
we have drawn it in orange colour in the figure below
Solution
We know vertically opposite angles are equal therefore, angle WZX and angle CZD are vertically opposite angles. Therefore they are equal as we have measured angle WZX is 82° so measure angle CZD is also 82°
[tex]\angle WZX = \angle CZD = 82[/tex]
Now measure angle BDC is 56° given so that is also same as measure angle CDZ
[tex]\angle BDC = \angle CDZ = 56[/tex]
Now in triangle CZD we have SUM of the all the measures of angle is 180° by Triangle property. Therefore,
[tex]\angle CZD + \angle CDZ + \angles ZCD = 180[/tex]
Now substituting the values of angle CZD = 82° and angle CDZ = 56° we get,
[tex]82 + 56 + \angle ZCD = 180\\138 + \angle ZCD = 180\\\angle ZCD = 180 - 138\\\angle ZCD = 42[/tex]
But angle ZCD is the same angle ACD. Therefore both are same
[tex]\angle ZCD = \angle ACD =42\\\angle ACD = 42[/tex]
