Question

If AB || DE, ∠AOD = ${50}^{\circ }$ and ∠DPC = ${160}^{\circ }$, find the value of ∠DBE?

• A. 50°​
• B. 60°​
• C. 120°​
• D. 160°​

Answer 1

The correct option is B

60°​

∠PCE = ${160}^{\circ }$​ – ${90}^{\circ }$​ = ${70}^{\circ }$​ (Exterior Angle Property)
In Δ ABC, ∠CAB = ${180}^{\circ }$ – ( ${90}^{\circ }$ + ${70}^{\circ }$​) = ${20}^{\circ }$​ (Angle Sum Property)
∠OBA = ${50}^{\circ }$ – ${20}^{\circ }$ = ${30}^{\circ }$ (Exterior Angle Property)
∠DBE = ${90}^{\circ }$ - ${30}^{\circ }$ = ${60}^{\circ }$