58 \(\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ\) [Angle sum property of triangle] \( \Rightarrow 50^\circ+72^\circ+\angle \text{C}=180^\circ\) \(\Rightarrow \angle \text{C}+122^\circ=180^\circ\) \(\Rightarrow \angle \text{C}=58^\circ\) Now, \(\text{x}^\circ=\angle\text{C}\) [Vertically opposite angles] \(\Rightarrow \text{x}^\circ= 58^\circ\) \(\Rightarrow \text{x}=58\) Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298359
In any \(\triangle\text{ABC},\text{AB}+\text{BC}+\text{CA}\) is________________
1 \(\text{Less than}\frac{1}{3}\text{AB}\)
2 \(\text{Equal to}\frac{1}{2}\text{AB}\)
3 \(\text{Less than}\text{ AB}\)
4 \(\text{Greater than}\text{ 2AB}\)
Explanation:
\(\text{Greater than}\text{ 2AB}\) In any Triangle, the sum of any two sides is always greater than the other side.in \(\triangle\text{ABC},\text{AB}+\text{BC}>\text{CA}....\text{eqn(1)}\) \(\text{BC + CA > AB}.....\text{eqn}(2)\) \(\text{CA + AB > BC}...\text{eqn}(3)\) In equation (2), adding AB both side we get, \(\text{AB + BC + CA > 2AB}\)
58 \(\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ\) [Angle sum property of triangle] \( \Rightarrow 50^\circ+72^\circ+\angle \text{C}=180^\circ\) \(\Rightarrow \angle \text{C}+122^\circ=180^\circ\) \(\Rightarrow \angle \text{C}=58^\circ\) Now, \(\text{x}^\circ=\angle\text{C}\) [Vertically opposite angles] \(\Rightarrow \text{x}^\circ= 58^\circ\) \(\Rightarrow \text{x}=58\) Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298359
In any \(\triangle\text{ABC},\text{AB}+\text{BC}+\text{CA}\) is________________
1 \(\text{Less than}\frac{1}{3}\text{AB}\)
2 \(\text{Equal to}\frac{1}{2}\text{AB}\)
3 \(\text{Less than}\text{ AB}\)
4 \(\text{Greater than}\text{ 2AB}\)
Explanation:
\(\text{Greater than}\text{ 2AB}\) In any Triangle, the sum of any two sides is always greater than the other side.in \(\triangle\text{ABC},\text{AB}+\text{BC}>\text{CA}....\text{eqn(1)}\) \(\text{BC + CA > AB}.....\text{eqn}(2)\) \(\text{CA + AB > BC}...\text{eqn}(3)\) In equation (2), adding AB both side we get, \(\text{AB + BC + CA > 2AB}\)
58 \(\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ\) [Angle sum property of triangle] \( \Rightarrow 50^\circ+72^\circ+\angle \text{C}=180^\circ\) \(\Rightarrow \angle \text{C}+122^\circ=180^\circ\) \(\Rightarrow \angle \text{C}=58^\circ\) Now, \(\text{x}^\circ=\angle\text{C}\) [Vertically opposite angles] \(\Rightarrow \text{x}^\circ= 58^\circ\) \(\Rightarrow \text{x}=58\) Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298359
In any \(\triangle\text{ABC},\text{AB}+\text{BC}+\text{CA}\) is________________
1 \(\text{Less than}\frac{1}{3}\text{AB}\)
2 \(\text{Equal to}\frac{1}{2}\text{AB}\)
3 \(\text{Less than}\text{ AB}\)
4 \(\text{Greater than}\text{ 2AB}\)
Explanation:
\(\text{Greater than}\text{ 2AB}\) In any Triangle, the sum of any two sides is always greater than the other side.in \(\triangle\text{ABC},\text{AB}+\text{BC}>\text{CA}....\text{eqn(1)}\) \(\text{BC + CA > AB}.....\text{eqn}(2)\) \(\text{CA + AB > BC}...\text{eqn}(3)\) In equation (2), adding AB both side we get, \(\text{AB + BC + CA > 2AB}\)
58 \(\angle \text{A}+\angle \text{B}+\angle \text{C}=180^\circ\) [Angle sum property of triangle] \( \Rightarrow 50^\circ+72^\circ+\angle \text{C}=180^\circ\) \(\Rightarrow \angle \text{C}+122^\circ=180^\circ\) \(\Rightarrow \angle \text{C}=58^\circ\) Now, \(\text{x}^\circ=\angle\text{C}\) [Vertically opposite angles] \(\Rightarrow \text{x}^\circ= 58^\circ\) \(\Rightarrow \text{x}=58\) Hence, the correct answer is option (c).
THE TRIANGLE AND ITS PROPERTIES
298359
In any \(\triangle\text{ABC},\text{AB}+\text{BC}+\text{CA}\) is________________
1 \(\text{Less than}\frac{1}{3}\text{AB}\)
2 \(\text{Equal to}\frac{1}{2}\text{AB}\)
3 \(\text{Less than}\text{ AB}\)
4 \(\text{Greater than}\text{ 2AB}\)
Explanation:
\(\text{Greater than}\text{ 2AB}\) In any Triangle, the sum of any two sides is always greater than the other side.in \(\triangle\text{ABC},\text{AB}+\text{BC}>\text{CA}....\text{eqn(1)}\) \(\text{BC + CA > AB}.....\text{eqn}(2)\) \(\text{CA + AB > BC}...\text{eqn}(3)\) In equation (2), adding AB both side we get, \(\text{AB + BC + CA > 2AB}\)
3