VSAQS
Page-11.29
Question 1:
Define a triangle.
Answer 1:
A plane figure bounded by three lines in a plane is called a triangle. A triangle has three sides, three angles and three vertices. The figure below represents a ΔABC, with AB, BC and CA as the three sides; ∠A, ∠B and ∠C as the three angles; A, B and C as the three vertices.

Question 2:
Write the sum of the angles of an obtuse triangle.
Answer 2:
In the given problem, ΔABC is an obtuse triangle, with
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,

Therefore, sum of the angles of an obtuse triangle is
.
Question 3:
In Δ ABC, if u∠B = 60°, ∠C = 80° and the bisectors of angles ∠ABC and ∠ACB meet at a point O, then find the measure of ∠BOC.
Answer 3:
In ΔABC,
,
and the bisectors of
and
meet at O.
We need to find the measure of 

Since,BO is the bisector of 

Similarly,CO is the bisector of 

Now, applying angle sum property of the triangle, in ΔBOC, we get,

Therefore,
.
Question 4:
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
Answer 4:
In the given problem, angles of ΔABC are in the ratio 2:1:3
We need to find the measure of the smallest angle.

Let,



According to the angle sum property of the triangle, in ΔABC, we get,

Thus,



Since, the measure of
is the smallest of all the three angles.
Therefore, the measure of the smallest angle is
.
Question 5:
State exterior angle theorem.
Answer 5:
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 ΔABC

Question 6:
The sum of two angles of a triangle is equal to its third angle. Determine the measure of the third angle.
Answer 6:
In the given problem, the sum of two angles of a triangle is equal to its third angle.
We need to find the measure of the third angle.

Thus, it is given, in 
........(1)
Now, according to the angle sum property of the triangle, we get,

(Using 1)

Therefore, the measure of the third angle is
.
Question 7:
In the given figure, if AB || CD, EF || BC, ∠BAC = 65° and ∠DHF = 35°, find ∠AGH.
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Answer 7:
In the given figure,
,
,
and 
We need to find
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Here, GF and CD are straight lines intersecting at point H, so using the property, “vertically opposite angles are equal”, we get,


Further, as
and AC is the transversal
Using the property, “alternate interior angles are equal”


Further applying angle sum property of the triangle
In ΔGHC

Hence, applying the property, “angles forming a linear pair are supplementary”
As AGC is a straight line

Therefore,
Question 8:
In the given figure, if AB || DE and BD || FG such that ∠FGH = 125° and ∠B = 55°, find x and y.

Answer 8:
In the given figure,
,
,
and 
We need to find the value of x and y

Here, as
and BD is the transversal, so according to the property, “alternate interior angles are equal”, we get

Similarly, as
and DF is the transversal

(Using 1)
Further, EGH is a straight line. So, using the property, angles forming a linear pair are supplementary

Also, using the property, “an exterior angle of a triangle is equal to the sum of the two opposite interior angles”, we get,
In
with
as its exterior angle

Thus,
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