Question 12 Marks
Can a triangle have: 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^\circ $ angle.
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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 $60^\circ ?$ Justify your answer in case.
Answer
View full question & answer→Yes, A triangle can have three angles equal to $60^{\circ}$. Then the sum of three angles equal to the $180^{\circ}$. Such triangles are called as equilateral triangle. [Since, the sum of all the internal angles of a triangle is $180^{\circ}$ ].
Question 42 Marks
Can a triangle have: All angles more than $60^\circ ?$ Justify your answer in case.
Answer
View full question & answer→No, Having angles more than $60^{\circ}$ make that sum more than $180^{\circ}$. This is not possible. [Since the sum of all the internal angles of a triangle is $180^{\circ}$ ]
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 $180^{\circ}$. So, $\angle A +\angle B +\angle C =180^{\circ}$ Therefore, sum of the angles of an obtuse triangle is $180^{\circ}$.
So, according to "the angle sum property of the triangle", for any kind of triangle, the sum of its angles is $180^{\circ}$. So, $\angle A +\angle B +\angle C =180^{\circ}$ Therefore, sum of the angles of an obtuse triangle is $180^{\circ}$.
Question 62 Marks
Can a triangle have: All angles less than $60^{\circ}$ ? Justify your answer in case.
Answer
View full question & answer→No, Having all angles less than $60^{\circ}$ will make that sum less than $180^{\circ}$ which is not possible. [Therefore, the sum of all the internal angles of a triangle is $180^{\circ}$ ]
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]
Question 82 Marks
Can a triangle have: 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 $90^{\circ}$ So that the sum of the two sides will exceed $180^{\circ}$ which is not possible. As the sum of all three angles of a triangle is $180^{\circ}$.
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.
Answer
View full question & answer→No, Two right angles would up to $180^\circ $. 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 $180^\circ ].$
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.
$\therefore\angle\text{X}+\angle\text{Y}+\angle\text{Z}$
$\Rightarrow\angle\text{X}+\angle\text{X}<\angle\text{X}+\angle\text{Y}+\angle\text{Z}$
$\Rightarrow2\angle\text{X}<180^\circ$ [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.
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]
$\angle\text{ACB}=180^\circ-112^\circ=68^\circ$ [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]
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]