Question

Lines AC←→ and DB←→ intersect at point W. Also, m∠DWC=138° .

Answer 1

m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°

Solution:

Line $\overrightarrow{A C} \text { and } \overrightarrow{B D}$ intersect at a point W.

Given $m \angle D W C=138^{\circ}$.

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°.