In ΔXYZ, points P, Q and R are points on the sides XY, YZ and XZ respectively ∠YXZ = 50 degree, XR = PR, ZR = QR and ∠RQZ = 80 degree. What is the value of ∠PRQ?
Answer & explanation
Correct answer: option 1
In \(\Delta \)XPR,
\(\angle\)PXR = \({50}^\circ\)
PR = XR
Therefore, triangle is isosceles
\(\angle\)XPR = \(\angle\)PXR = 50
\(\angle\)XPR = 180 - 50 - 50
\(\angle\)XPR = \({80}^\circ\)
Similarly,
= \(\angle\)RQZ = \(\angle\)RZQ = 80
= \(\angle\)QRZ = 180 - 80 - 80
= \(\angle\)QRZ = \({20}^\circ\)
Now,
\(\angle\)PRQ = 180 - 20 - 80 = \({80}^\circ\).
Therefore, \(\angle\)PRQ is \({80}^\circ\).