TEST 1
1.
\([CA]\perp[AD]\)
\(|CD|=z\)
\(|BD|=x\)
\(|AD|=y\)
Which one of the following is correct?
A) \(x>y>z\)B) \(z>x>y\)C) \(y>x>z\)D) \(y>z>x\)E) \(x>z>y\)
2.
\(x\in\mathbb{Z}\)
\(m\left(\widehat{BAC}\right)=100^\circ\)
\(|AB|=13\text{ br}\)
\(|BC|=x+6\)
\(\Rightarrow\min\left(x\right)=?\)
A) \(6\)B) \(7\)C) \(8\)D) \(9\)E) \(10\)
3.
\(x\in\mathbb{Z}\)
\(m\left(\widehat{ABC}\right)=m\left(\widehat{CBD}\right)\)
\(|BD|=10\text{ br}\)
\(|CD|=2x\)
\(\Rightarrow\max\left(x\right)=?\)
A) \(6\)B) \(5\)C) \(4\)D) \(3\)E) \(2\)
4.
\(x\in\mathbb{Z}\)
\(m\left(\widehat{ABC}\right)=m\left(\widehat{CBD}\right)\)
\(m\left(\widehat{BAD}\right)=70^\circ\)
\(m\left(\widehat{BCA}\right)=95^\circ\)
\(\Rightarrow\max\left(x\right)=?\)
A) \(15\)B) \(14\)C) \(13\)D) \(12\)E) \(11\)
5.
\(x\in\mathbb{Z}\)
\(m\left(\widehat{ABC}\right)=m\left(\widehat{CBD}\right)\)
\(|BD|=7\text{ br}\)
\(|CD|=x+4\)
\(\Rightarrow\min\left(x\right)=?\)
A) \(3\)B) \(4\)C) \(5\)D) \(6\)E) \(7\)
6.
\(|AB|=|AC|\)
\(20^\circ<m\left(\widehat{B}\right)<60^\circ\)
\(m\left(\widehat{BAC}\right)=\alpha\)
What is the definition range of \(\alpha\)?
A) \(60^\circ<\alpha<140^\circ\)B) \(60^\circ<\alpha<120^\circ\)C) \(40^\circ<\alpha<140^\circ\)D) \(40^\circ<\alpha<60^\circ\)E) \(40^\circ<\alpha<120^\circ\)
7.
\(\alpha\in\mathbb{Z}\)
\(|AC|=|AD|\)
\(m\left(\widehat{ABD}\right)=44^\circ\)
\(m\left(\widehat{BAC}\right)=\alpha\)
\(\Rightarrow\max\left(\alpha\right)=?\)
A) \(44\)B) \(45\)C) \(46\)D) \(47\)E) \(48\)
8.
\(\alpha\in\mathbb{Z}\)
\(|AB|=|BC|\)
\(m\left(\widehat{A}\right)>50^\circ\)
\(m\left(\widehat{ABC}\right)=\alpha\)
\(\Rightarrow\max\left(\alpha\right)=?\)
A) \(80\)B) \(81\)C) \(77\)D) \(78\)E) \(79\)