Question

In the figure,
`\angle` AOB =
`(1)/(2)`
`\angle` BOC and
`\angle` BOC =
`(2)/(3)`
`\angle` COD . Show that
`\angle` COD =
`(1)/(2) \angle` AOD mentioning necessary axioms.

~Thanks in advance !

Answer 1

this is your answer. good luck.

Answer 2

See Below.

Explanation:

Statements: Reasons:

`1)\text{ }\angle AOD=180` Straight Angle Theorem

`2)\text{ } \angle AOB+\angle BOC+\angle COD=\angle AOD` Angle Addition

`3)\text{ } \angle AOB+\angle BOC+\angle COD=180` Substitution

`\displaystyle 4)\text{ } \angle AOB=(1)/(2)\angle BOC` Given

`\displaystyle 5)\text{ } \angle BOC=(2)/(3)\angle COD` Given

`\displaystyle 6)\text{ } (1)/(2)\angle BOC+(2)/(3)\angle COD+\angle COD=180` Substitution

`\displaystyle 7)\text{ } (1)/(2)\Big((2)/(3)\angle COD\Big)+(2)/(3)\angle COD+\angle COD=180` Substitution

`\displaystyle 8)\text{ } (1)/(3)\angle COD+(2)/(3)\angle COD+\angle COD=180` Multiplication

`\displaystyle 9)\text{ } 2\angle COD=180` Addition

`10)\text{ } \angle COD=90` Division Property of Equality

`\displaystyle 11)\text{ } (1)/(2)\angle AOD=90` Division Property of Equality

`\displaystyle 12)\text{ } \angle COD=(1)/(2)\angle AOD` Substitution