Question

[Vũ Bảo Nam]

Answer 1

[Nguyễn Lê Phước Thịnh]

a: Xét tứ giác ABCD có \(\widehat{A}+\widehat{B}+\widehat{C}+\widehat{D}=360^0\)

=>\(\widehat{C}+\widehat{D}=360^0-110^0-70^0=180^0\)

=>\(\dfrac{1}{3}\cdot\widehat{D}+\widehat{D}=180^0\)

=>\(\dfrac{4}{3}\cdot\widehat{D}=180^0\)

=>\(\widehat{D}=135^0\)

\(\widehat{C}=\dfrac{1}{3}\cdot135^0=45^0\)

b:

Sửa đề: Cho tứ giác ABCD.

Đặt \(\widehat{B}=x;\widehat{C}=y;\widehat{D}=z\)

\(\dfrac{\widehat{B}}{2}=\dfrac{\widehat{C}}{3}=\dfrac{\widehat{D}}{4}\)

=>\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}\)

Xét tứ giác ABCD có \(\widehat{A}+\widehat{B}+\widehat{C}+\widehat{D}=360^0\)

=>\(x+y+z=360^0-90^0=270^0\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x+y+z}{2+3+4}=\dfrac{270}{9}=30^0\)

=>\(x=2\cdot30^0=60^0;y=3\cdot30^0=90^0;z=4\cdot30^0=120^0\)

Vậy: \(\widehat{B}=x=60^0;\widehat{C}=y=90^0;\widehat{D}=z=120^0\)