Ta có; \(\hat{AOC}+\hat{BOC}=180^0\) (hai góc kề bù)

=>\(5\cdot\hat{BOC}+\hat{BOC}=180^0\)

=>\(6\cdot\hat{BOC}=180^0\)

=>\(\hat{BOC}=30^0\)

=>\(\hat{AOC}=5\cdot30^0=150^0\)

Ta có: \(\hat{AOC}=\hat{BOD}\) (hai góc đối đỉnh)

mà \(\hat{AOC}=150^0\)

nên \(\hat{BOD}=150^0\)

Ta có: \(\hat{BOC}=\hat{AOD}\) (hai góc đối đỉnh)

mà \(\hat{BOC}=30^0\)

nên \(\hat{AOD}=30^0\)

A O C D B

TH1: \(\widehat{AOC}+\widehat{AOD}+\widehat{BOD}=230o\)

Mà \(\widehat{AOC}=\widehat{BOD}\) (2 góc đối đỉnh)

=> \(2.\widehat{AOC}+\widehat{AOD}=230o\)

Mà \(\widehat{AOC}+\widehat{AOD}=180o\) (2 góc kề bù)

=> \(\left\{{}\begin{matrix}\widehat{AOC}=\widehat{BOD}=50o\\\widehat{AOD}=\widehat{BOC}=130o\end{matrix}\right.\)

TH2: \(\widehat{AOD}+\widehat{BOD}+\widehat{BOC}=230o\)

Mà \(\widehat{AOD}=\widehat{BOC}\) (2 góc đối đỉnh)

=> \(2.\widehat{AOD}+\widehat{BOD}=230o\)

Mà \(\widehat{AOD}+\widehat{BOD}=180o\)

=> \(\left\{{}\begin{matrix}\widehat{AOD}=\widehat{BOC}=50o\\\widehat{BOD}=\widehat{AOC}=130o\end{matrix}\right.\)

vô lí do \(\widehat{AOC}>\widehat{BOC}\)

Sửa đề: ab và cd cắt nhau tại O

Ta có: \(\hat{aOc}+\hat{bOc}=180^0\) (hai góc kề bù)

=>\(4\cdot\hat{bOc}+\hat{bOc}=180^0\)

=>\(5\cdot\hat{bOc}=180^0\)

=>\(\hat{bOc}=\frac{180^0}{5}=36^0\)

=>\(\hat{aOc}=36^0\cdot4=144^0\)

Ta có: \(\hat{aOc}=\hat{bOd}\) (hai góc đối đỉnh)

mà \(\hat{aOc}=144^0\)

nên \(\hat{bOd}=144^0\)

ta có: \(\hat{bOc}=\hat{aOd}\) (hai góc đối đỉnh)

mà \(\hat{bOc}=36^0\)

nên \(\hat{aOd}=36^0\)

Ta có: \(\hat{AOC}+\hat{BOC}=180^0\) (hai góc kề bù)

=>\(4\cdot\hat{BOC}+\hat{BOC}=180^0\)

=>\(5\cdot\hat{BOC}=180^0\)

=>\(\hat{BOC}=36^0\)

=>\(\hat{AOC}=4\cdot36^0=144^0\)

Ta có: \(\hat{AOC}=\hat{BOD}\) (hai góc đối đỉnh)

mà \(\hat{AOC}=144^0\)

nên \(\hat{BOD}=144^0\)

Ta có: \(\hat{BOC}=\hat{AOD}\) (hai góc đối đỉnh)

mà \(\hat{BOC}=36^0\)

nên \(\hat{AOD}=36^0\)

$a)$ $\widehat{AOC}$; $\widehat{AOD}$; $\widehat{DOB}$; $\widehat{COB}$

$b)$ $\widehat{BOC}$=$180$-$\widehat{COA}$=$180-50=130$

$\Rightarrow$ $\widehat{BOD=50}$ ( đối đỉnh với $\hat{A}$