True False[1 Marks ]

Question 11 Mark

The following statements are true $(T)$ and which are false $(F):$
An exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Answer

True.
Explanation:

According to exterior angle theorem,
$\text{ext.x}=\angle\text{CAB}+\angle\text{CBA}$

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Question 21 Mark

The following statements are true $(T)$ and which are false $(F):$
An exterior angle of a triangle is greater than the opposite interior angles.

Answer

True.
Explanation:

According to exterior angle theorem,
$\text{ext.x}=\angle\text{CAB}+\angle\text{CBA}$
Since, the exterior angle is the sum of its interior angels.
Thus,
$\text{ext.x}>\angle\text{CAB}$
$\text{ext.x}>\angle\text{CBA}$

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Question 31 Mark

The following statements are true $(T)$ and which are false $(F):$ Sum of the three angles of a triangle is $180^\circ .$

Answer

True. Explanation:

According to the angle sum property of the triangle In $\triangle\text{ABC}$ $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$

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Question 41 Mark

The following statements are true $(T)$ and which are false $(F): $ All the angles of a triangle can be equal to $60^\circ .$

Answer

According to the angle sum property of the triangle In $\triangle\text{ABC}$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Now, if all the three angles of a triangle are equal to $60^\circ $
Then, $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$

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Question 51 Mark

The following statements are true $(T)$ and which are false $(F):$ A triangle can have two obtuse angles.

Answer

According to the angle sum property of the triangle In$\triangle\text{ABC}$ $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Now, if a triangle of a triangle are equal to $60^\circ $
Then, $\angle\text{A}+\angle\text{B}+\angle\text{C}>180^\circ$

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Question 61 Mark

The following statements are true $(T)$ and which are false $(F):$
A triangle can have two right angles.

Answer

According to the angle sum property of the triangle
In $\triangle\text{ABC}$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Now, if there are two right angles in the triangle
Let $\angle\text{B}=\angle\text{C}=90^\circ$
Then,
$\angle\text{A}+90^\circ+90^\circ=180^\circ$
$\angle\text{A}+180^\circ=180^\circ$
$\angle\text{A}=180^\circ-180^\circ$
$\angle\text{A}=0^\circ$
(This is not possible.)

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Question 71 Mark

The following statements are true $(T)$ and which are false $(F):$ All the angles of a triangle can be less than $60^\circ .$

Answer

: According to the angle sum property of the triangle In $\triangle\text{ABC}$ $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Now, If all the three angles of a triangle is less than $60^\circ$
Then, $\angle\text{A}+\angle\text{B}+\angle\text{C}<180^\circ$

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Question 81 Mark

The following statements are true $(T)$ and which are false $(F):$ If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

Answer

According to the angle sum property of the triangle In $\triangle\text{ABC}$ $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Now, if a right angled triangle
Then, $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
$90^\circ+\angle\text{B}+\angle\text{C}=180^\circ$
$\angle\text{B}+\angle\text{C}=90^\circ$
Also if one of the angle's is obtuse $\angle\text{B}+\angle\text{C}>90^\circ$ This is not possible.
Thus, if one angle of a triangle is obtuse, then it cannot be a right angled triangle.

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Question 91 Mark

The following statements are true $(T)$ and which are false $(F):$ An exterior angle of a triangle is less than either of its interior opposite angles.

Answer

According to the exterior angle property, an exterior angle of a equal to the sum of the two opposite interior angles.

In $\triangle\text{ABC}$
Let $x$ be the exterior angle
So, $\text{x}=\angle\text{CAB}+\angle\text{CBA}$
Now, if $x$ is less than either of its interior opposite angles $\text{x}<\angle\text{CAB}+\angle\text{CBA}$

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Question 101 Mark

Which of the following statements are true $(T)$ and which are false $(F):$ A triangle can have at most one obtuse angles.

Answer

According to the angle sum property of the triangle In $\triangle\text{ABC}$ $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Now, if a triangle will have more than one obtuse angle
Then, $\angle\text{A}+\angle\text{B}+\angle\text{C}>180^\circ$

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Question 111 Mark

The following statements are true $(T)$ and which are false $(F):$ All the angles of a triangle can be greater than $60^\circ .$

Answer

According to the angle sum property of the triangle In
$\triangle\text{ABC}$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
Now, if all the three angles of a triangle is greater than $60^\circ $
Then, $\angle\text{A}+\angle\text{B}+\angle\text{C}>180^\circ$

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