$2. PQRST is a regular pentagon. If PR and
QT intersects each other at x, then what
is the value (in degrees) of ZTXR?
PQRST एक सम पंचभुज है। यदि PR तथा T
एक-दूसरे को X पर प्रतिच्छेद करते है तो/TXR का
मान (डिग्री में) क्या है?
(a) 98
(b) 90
(c) 72
(d) 108
Answers
Given : PQRST is a regular pentagon. If PR and QT intersects each other at x
To Find : what is the value (in degrees) of ∠TXR
Solution:
PQRST is Pentagon
Each Integral angle = 108°
PQ = QR = RS = ST = TR
=> in Δ PQR
PQ = QR & ∠ Q = 108°
∠QPR = ∠QRP
=> ∠QPR = ( 180° - 108° )/2 = 36°
Similarly ∠PQT = 36°
∠QPR + ∠PQT + ∠PXQ = 180°
36° + 36° + ∠PXQ = 180°
=> ∠PXQ = 108°
∠TXR = ∠PXQ Vertically opposite angles
=> ∠TXR = 108°
value (in degrees) of ∠TXR = 108
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Answer:
Step-by-step explanation:
Internal angle in a regular Pentagon will be 108 degree.angle RPQ and angle QTP are equal. Moreover triangle PQR and QTP are similar triangles, QT and PR are diagonals of regular Pentagon.
