Question

In the given figure, if D and E are the points on the base QR of ΔPQR such that DQ = ER, PD = PE and ∠DPR = 50°, then the measure of ∠QPE is

• A. 40°
• B. 50°
• C. 70°
• D. 60°

Answer 1

The correct option is B 50°

In ΔPDE, PD = DE
Since angles opposite to equal sides are equal.
∴ ∠PDE = ∠PED …..(i)
Now, QD = ER,
⇒ QD + DE = ER + DE
⇒ QE = DR …..(ii)
In ΔQPE and ΔRPD,
PE = PD (Given)
∠PEQ = ∠PDR [From (i)]
QE = RD [From (ii)]
∴ ΔQPE ≅ ΔRPD (SAS congruence rule)
⇒ ∠QPE = ∠RPD (CPCT)
⇒ ∠QPE = 50° (∵ ∠RPD = 50°)
Hence, the correct answer is option (b).