Question

The rays oa, ob, oc, od, and ob have the common initial point o. Show that angle aob+angle boc +angle cod+ angle boa=360degree.(hint draw a ray opposite to ray oa)

Answer 1

$\huge\star{\underline{\mathfrak{Answer}}}$

Given:The rays oa, ob, oc, od and oe have the common initial point o.

Construction:draw OP ray opposite to OA.

PROOF:

<AOB+<DOE+<COP = 180

(0A is a line)..........(1)

<POD+<DOE+<EOA = 180

(OA is a line)..........(2)

Add (1) and (2)

<AOB+<BOC+( <COP + <POD ) + <DOE+<EOA = 180+ 180

<AOB +<BOC + <COD + < DOE +<EOA = 360.

a+b+c+d+e = 360°.