48. In /_\XYZ, XY = XZ. A straight line cuts XZ at P, YZ
at Q and XY produced at R. If YQ = YR and
QP = QZ, then the measure of
/_PQY is
(a) 100°
(b) 124°
(C) 144°
(d) 140°
Answers
Given : in Δ XYZ XY = XZ. A straight line cuts XZ at P, YZ at Q and XY produced at R. YQ = YR and QP = QZ,
To find : the measure of ∠PQY
Solution:
XY = XZ
=> ∠XYZ = ∠XZY = A
∠XYZ = ∠XYQ = A is exterior angle of triangle YQR
YQ = YR => ∠YRQ = ∠YQR
∠XYQ = ∠YRQ + ∠YQR => A = 2 ∠YQR
=> ∠YQR = A/2
∠YQR = ∠PQZ
=> ∠PQZ = A/2
in triangle PQZ QP = QZ
=> ∠QPZ = ∠QZP = A
∠PQZ + ∠QPZ + ∠QZP = 180°
=> A/2 + A + A = 180°
=> 5A = 360°
=> A = 72°
=> A/2 = 36°
∠PQY = 180° - ∠PQZ = 180° - A/2
=>∠PQY = 180° - 36°
=> ∠PQY = 144°
option C is correct
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Answer:
XY = XZ
=> ∠XYZ = ∠XZY = A
∠XYZ = ∠XYQ = A is exterior angle of triangle YQR
YQ = YR => ∠YRQ = ∠YQR
∠XYQ = ∠YRQ + ∠YQR => A = 2 ∠YQR
=> ∠YQR = A/2
∠YQR = ∠PQZ
=> ∠PQZ = A/2
in triangle PQZ QP = QZ
=> ∠QPZ = ∠QZP = A
∠PQZ + ∠QPZ + ∠QZP = 180°
=> A/2 + A + A = 180°
=> 5A = 360°
=> A = 72°
=> A/2 = 36°
∠PQY = 180° - ∠PQZ = 180° - A/2
=>∠PQY = 180° - 36°
=> ∠PQY = 144°
Step-by-step explanation: