Question 12 Marks
Can a triangle have:
Two acute angles?
Justify your answer in case.
Two acute angles?
Justify your answer in case.
Answer
View full question & answer→Yes, A triangle can have 2 acute angles. Acute angle means less the 90° angle.
Questions
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Question 22 Marks
Define a triangle.
Answer
View full question & answer→A plane figure bouded by three lines in a plane is called a triangle. The figure below represent a $\triangle\text{ABC},$ with AB, AC and BC as the three segments.
Question 32 Marks
Can a triangle have:
All angles equal to 60°?
Justify your answer in case.
All angles equal to 60°?
Justify your answer in case.
Answer
View full question & answer→Yes, A triangle can have three angles equal to 60°. Then the sum of three angles equal to the 180°. Such triangles are called as equilateral triangle. [Since, the sum of all the internal angles of a triangle is180°].
Question 42 Marks
Can a triangle have:
All angles more than 60°?
Justify your answer in case.
All angles more than 60°?
Justify your answer in case.
Answer
View full question & answer→No, Having angles more than 60° make that sum more than 180°. This is not possible. [Since the sum of all the internal angles of a triangle is 180°]
Question 52 Marks
Write the sum of the angles of an obtuse triangle.
Answer
View full question & answer→In the given problem, $\triangle\text{ABC}$ is an obtuse triangle, with$\angle\text{B}$ as the obtuse angle. 
So, according to "the angle sum property of the triangle", for any kind of triangle, the sum of its angles is 180°. So,$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Therefore, sum of the angles of an obtuse triangle is 180º.
So, according to "the angle sum property of the triangle", for any kind of triangle, the sum of its angles is 180°. So,$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$Therefore, sum of the angles of an obtuse triangle is 180º.
Question 62 Marks
Can a triangle have:
All angles less than 60°?
Justify your answer in case.
All angles less than 60°?
Justify your answer in case.
Answer
View full question & answer→No, Having all angles less than 60° will make that sum less than 180° which is not possible. [Therefore, the sum of all the internal angles of a triangle is 180°]
Question 72 Marks
Compute the value of x in the following figures.
Answer
View full question & answer→$\angle\text{ABC}=180^\circ-120^\circ=60^\circ$ [Linear pair]$\angle\text{ACB}=180^\circ-110^\circ=70^\circ$ [Linear pair]
$\therefore\text{e}\angle\text{BAC}=\text{x}$
$=180^\circ-\angle\text{ABC}-\angle\text{ACB}=180^\circ-60^\circ-70^\circ=50^\circ$ [Sum of all angles of a triangle]
$\therefore\text{e}\angle\text{BAC}=\text{x}$
$=180^\circ-\angle\text{ABC}-\angle\text{ACB}=180^\circ-60^\circ-70^\circ=50^\circ$ [Sum of all angles of a triangle]
Question 82 Marks
Can a triangle have:
Two obtuse angles?
Justify your answer in case.
Two obtuse angles?
Justify your answer in case.
Answer
View full question & answer→No, A triangle can't have 2 obtuse angles. Obtuse angle means more than 90° So that the sum of the two sides will exceed 180° which is not possible. As the sum of all three angles of a triangle is 180°.
Question 92 Marks
State exterior angle theorem.
Answer
View full question & answer→Exterior angle theorem states that, if a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles. 
Thus, in $\triangle\text{ABC}$$\angle\text{ACD}=\angle\text{A}+\angle\text{B}$
Thus, in $\triangle\text{ABC}$$\angle\text{ACD}=\angle\text{A}+\angle\text{B}$Question 102 Marks
Can a triangle have:
Two right angles?
Justify your answer in case.
Two right angles?
Justify your answer in case.
Answer
View full question & answer→No, Two right angles would up to 180°. So the third angle becomes zero. This is not possible, so a triangle cannot have two right angles. [Since sum of angles in a triangle is 180°].
Question 112 Marks
If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.
Answer
View full question & answer→Given each angle of a triangle less than the sum of the other two$\therefore\angle\text{X}+\angle\text{Y}+\angle\text{Z}$
$\Rightarrow\angle\text{X}+\angle\text{X}<\angle\text{X}+\angle\text{Y}+\angle\text{Z}$
$\Rightarrow2\angle\text{X}<180^\circ$ [Sum of all the angles of a triangle]
$\Rightarrow\angle\text{X}<90^\circ$
Similarly $\angle\text{Y}<90^\circ$ and $\angle\text{Z}<90^\circ$ Hence, the triangles are acute angled.
$\Rightarrow\angle\text{X}+\angle\text{X}<\angle\text{X}+\angle\text{Y}+\angle\text{Z}$
$\Rightarrow2\angle\text{X}<180^\circ$ [Sum of all the angles of a triangle]
$\Rightarrow\angle\text{X}<90^\circ$
Similarly $\angle\text{Y}<90^\circ$ and $\angle\text{Z}<90^\circ$ Hence, the triangles are acute angled.
Question 122 Marks
Compute the value of x in the following figures.
Answer
View full question & answer→$\angle\text{BAC}=180^\circ-120^\circ=60^\circ$ [Linear pair]$\angle\text{ACB}=180^\circ-112^\circ=68^\circ$ [Linear pair]
$\therefore\text{x}=180^\circ-\angle\text{BAC}-\angle\text{ACB}$
$=180^\circ-60^\circ-68^\circ=52^\circ$ [Sum of all angles of a triangle]
$\therefore\text{x}=180^\circ-\angle\text{BAC}-\angle\text{ACB}$
$=180^\circ-60^\circ-68^\circ=52^\circ$ [Sum of all angles of a triangle]
Question 132 Marks
Compute the value of x in the following figures.
Answer
View full question & answer→$\angle\text{BAE}=\angle\text{EDC}=52^\circ$ [Alternate angles]$\therefore\angle\text{DEC}=\text{x}=180^\circ-40^\circ-\angle\text{EDC}$
$=180^\circ-40^\circ-52^\circ$
$=180^\circ-92^\circ=88^\circ$ [Sum of all angles of a triangle]
$=180^\circ-40^\circ-52^\circ$
$=180^\circ-92^\circ=88^\circ$ [Sum of all angles of a triangle]