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Question

Tính các góc của hình thang ABCD ( AB//CD) biết góc A = 1/3 góc D . Góc B - góc C = 50 độ

Nobi Nobita · Accepted Answer

A B C D

a) Vì ABCD là hình thang ( $AB//CD$)

$\Rightarrow\widehat{B}+\widehat{C}=180^o$

mà $\widehat{B}-\widehat{C}=50^o$$\Rightarrow\widehat{B}=\frac{180^o+50^o}{2}=115^o$

$\Rightarrow\widehat{C}=180^o-115^o=65^o$

Vì $AB//CD$$\Rightarrow\widehat{A}+\widehat{D}=180^o$

mà $\widehat{A}=\frac{1}{3}.\widehat{D}$$\Rightarrow\frac{1}{3}.\widehat{D}+\widehat{D}=180^o$

$\Rightarrow\frac{4}{3}.\widehat{D}=180^o$$\Rightarrow\widehat{D}=135^o$$\Rightarrow\widehat{A}=\frac{1}{3}.135^o=45^o$

Vậy $\widehat{A}=45^o$; $\widehat{B}=115^o$; $\widehat{C}=65^o$; $\widehat{D}=135^o$

Câu trả lời:

A B C D

a) Vì ABCD là hình thang ( $AB//CD$)

$\Rightarrow\widehat{B}+\widehat{C}=180^o$

mà $\widehat{B}-\widehat{C}=50^o$$\Rightarrow\widehat{B}=\frac{180^o+50^o}{2}=115^o$

$\Rightarrow\widehat{C}=180^o-115^o=65^o$

Vì $AB//CD$$\Rightarrow\widehat{A}+\widehat{D}=180^o$

mà $\widehat{A}=\frac{1}{3}.\widehat{D}$$\Rightarrow\frac{1}{3}.\widehat{D}+\widehat{D}=180^o$

$\Rightarrow\frac{4}{3}.\widehat{D}=180^o$$\Rightarrow\widehat{D}=135^o$$\Rightarrow\widehat{A}=\frac{1}{3}.135^o=45^o$

Vậy $\widehat{A}=45^o$; $\widehat{B}=115^o$; $\widehat{C}=65^o$; $\widehat{D}=135^o$

Nguyễn Việt Hoàng · Answer

Vì ABCD là hình thang ( AB // CD )

$\Rightarrow\hept{\begin{cases}\widehat{A}+\widehat{B}=180^o\\widehat{C}+\widehat{D}=180^o\end{cases}}$

$\Rightarrow\hept{\begin{cases}\widehat{B}=\left(180+50\right):2=165^o\\widehat{C}=165-50=95^o\end{cases}}$

+) $\widehat{A}=\frac{1}{3}\widehat{D}$

$\Rightarrow\widehat{D}=3\widehat{A}$

$\Rightarrow\widehat{A}+\widehat{D}=\widehat{A}+3\widehat{A}=4\widehat{A}=180^o$

$\Rightarrow\widehat{A}=180:4=45^o$

$\widehat{D}=3\widehat{A}=45.3=135^o$