m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°
Solution:
Line [tex]\overrightarrow{A C} \text { and } \overrightarrow{B D}[/tex] intersect at a point W.
Given [tex]m \angle D W C=138^{\circ}[/tex].
Vertical angle theorem:
If two lines intersect at a point then vertically opposite angles are congruent.
To find the measure of all the angles:
∠AWB and ∠DWC are vertically opposite angles.
Therefore, ∠AWB = ∠DWC
⇒ ∠AWB = 138°
Sum of all the angles in a straight line = 180°
⇒ ∠AWD + ∠DWC = 180°
⇒ ∠AWD + 138° = 180°
⇒ ∠AWD = 180° – 138°
⇒ ∠AWD = 42°
Since ∠AWD and ∠BWC are vertically opposite angles.
Therefore, ∠AWD = ∠BWC
⇒ ∠BWC = 42°
Hence the measure of the angles are
m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°.
