In the adjoining figure, the sides of triangle PQR are produced. Prove that angle XRP+ angle YPQ+ angle ZQR=360 .
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Step-by-step explanation:
<RPQ +<PQR + <QRP = 180° [ Angle sum property)
< XRP= <RPQ+ <PQR [ Exterior angle property] (1)
<YPQ= <PRQ + <RQP [Exterior angle property] (2)
<ZQR= <QRP + < RPQ [Exterior angle property] (3)
Substituting (1), (2) and (3)
<XRP + <YPQ + < ZQR = <RPQ+ <PQR + <PRQ + <RQP + <QRP + < RPQ
= <RPQ +<PQR + <QRP + <RPQ +<PQR + <QRP
= 180° + 180°
= 360°
Angle sum property : The sum of the interior angles of a triangle is 180°
Exterior angle property : The value of an exterior angle is the sum of the non- adjacent interior angles of the triangle.
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