298404
In a \(\triangle \text{ABC},\) if \(\angle \text{A}-\angle \text{B}=33^\circ\) and \(\angle \text{B}-\angle \text{C}=10^\circ,\) then \(\angle \text{B} =\)
1 35º
2 45º
3 55º
4 25º
Explanation:
25º \(\angle \text{A}-\angle \text{B}=33^\circ\) and \(\angle \text{B}-\angle \text{C}=18^\circ\) \(\Rightarrow \angle \text{A}=\angle \text{B}+33^\circ\) and \(\angle \text{C}=\angle \text{B}-18^\circ\) Now, \(\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow \angle \text{B}+33^\circ+\angle \text{B}+\angle \text{B}-18^\circ=180^\circ\) \(\Rightarrow 3\angle \text{B}+15^\circ=180^\circ\) \(\Rightarrow 3\angle \text{B}=165^\circ\) \(\Rightarrow \angle \text{B}=55^\circ\) Hence, the correct answer is option (d).
THE TRIANGLE AND ITS PROPERTIES
298405
Which of the following sets of measures cannot be the lengths of the sides of a right triangle?
298404
In a \(\triangle \text{ABC},\) if \(\angle \text{A}-\angle \text{B}=33^\circ\) and \(\angle \text{B}-\angle \text{C}=10^\circ,\) then \(\angle \text{B} =\)
1 35º
2 45º
3 55º
4 25º
Explanation:
25º \(\angle \text{A}-\angle \text{B}=33^\circ\) and \(\angle \text{B}-\angle \text{C}=18^\circ\) \(\Rightarrow \angle \text{A}=\angle \text{B}+33^\circ\) and \(\angle \text{C}=\angle \text{B}-18^\circ\) Now, \(\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow \angle \text{B}+33^\circ+\angle \text{B}+\angle \text{B}-18^\circ=180^\circ\) \(\Rightarrow 3\angle \text{B}+15^\circ=180^\circ\) \(\Rightarrow 3\angle \text{B}=165^\circ\) \(\Rightarrow \angle \text{B}=55^\circ\) Hence, the correct answer is option (d).
THE TRIANGLE AND ITS PROPERTIES
298405
Which of the following sets of measures cannot be the lengths of the sides of a right triangle?
298404
In a \(\triangle \text{ABC},\) if \(\angle \text{A}-\angle \text{B}=33^\circ\) and \(\angle \text{B}-\angle \text{C}=10^\circ,\) then \(\angle \text{B} =\)
1 35º
2 45º
3 55º
4 25º
Explanation:
25º \(\angle \text{A}-\angle \text{B}=33^\circ\) and \(\angle \text{B}-\angle \text{C}=18^\circ\) \(\Rightarrow \angle \text{A}=\angle \text{B}+33^\circ\) and \(\angle \text{C}=\angle \text{B}-18^\circ\) Now, \(\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow \angle \text{B}+33^\circ+\angle \text{B}+\angle \text{B}-18^\circ=180^\circ\) \(\Rightarrow 3\angle \text{B}+15^\circ=180^\circ\) \(\Rightarrow 3\angle \text{B}=165^\circ\) \(\Rightarrow \angle \text{B}=55^\circ\) Hence, the correct answer is option (d).
THE TRIANGLE AND ITS PROPERTIES
298405
Which of the following sets of measures cannot be the lengths of the sides of a right triangle?
298404
In a \(\triangle \text{ABC},\) if \(\angle \text{A}-\angle \text{B}=33^\circ\) and \(\angle \text{B}-\angle \text{C}=10^\circ,\) then \(\angle \text{B} =\)
1 35º
2 45º
3 55º
4 25º
Explanation:
25º \(\angle \text{A}-\angle \text{B}=33^\circ\) and \(\angle \text{B}-\angle \text{C}=18^\circ\) \(\Rightarrow \angle \text{A}=\angle \text{B}+33^\circ\) and \(\angle \text{C}=\angle \text{B}-18^\circ\) Now, \(\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ\) [Angle sum property of triangle] \(\Rightarrow \angle \text{B}+33^\circ+\angle \text{B}+\angle \text{B}-18^\circ=180^\circ\) \(\Rightarrow 3\angle \text{B}+15^\circ=180^\circ\) \(\Rightarrow 3\angle \text{B}=165^\circ\) \(\Rightarrow \angle \text{B}=55^\circ\) Hence, the correct answer is option (d).
THE TRIANGLE AND ITS PROPERTIES
298405
Which of the following sets of measures cannot be the lengths of the sides of a right triangle?
