Question

4. In Fig. 10.34.rays , 0A, OB, OC, OD and OE have the common end point O. Show that
ANGLE AOB + BOC + COD + DOE + EOA = 360°.​

Answer 1

Answer:

Construction:draw OP ray opposite to OA.

PROOF:

<AOB+<DOE+<COP = 180

(0A is a line)

<POD+<DOE+<EOA = 180

(OA is a line)

Add (1) and (2)

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

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

a+b+c+d+e = 360°.