Question

In the adjoining figure, the sides of triangle PQR are produced. Prove that angle XRP+ angle YPQ+ angle ZQR=360 .​

Answer 1

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.