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21 votes
21 votes
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 !

In the figure, \angle AOB = (1)/(2)\angle BOC and \angle BOC = (2)/(3)\angle COD . Show-example-1
User Verbatus
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2 Answers

7 votes
7 votes

Answer:

this is your answer. good luck.

In the figure, \angle AOB = (1)/(2)\angle BOC and \angle BOC = (2)/(3)\angle COD . Show-example-1
In the figure, \angle AOB = (1)/(2)\angle BOC and \angle BOC = (2)/(3)\angle COD . Show-example-2
User Nagaraj Raveendran
by
3.6k points
6 votes
6 votes

Answer:

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

User Tink
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