
Lines , and intersect at a common point as shown in figure. is joined to , to and to to form a triangle. The value of is is
A.
B.
C.
D.

Answer
419.7k+ views
Hint: In this problem we have to find the sum of the angles.
We will use the fact that the external angle of a triangle is equal to the sum of opposite two internal angles. For example: in the above figure is an external angle of triangle . Hence can be written as the sum of opposite two internal angles.
i.e.
Complete step by step solution:
This problem is based on triangles. Triangle is a closed figure bounded by a three line segment. A triangle has three vertices, three sides and three angles.
The given diagram is mentioned below,
Let us assume, the Sum of all the angles in a triangle is .
Consider the given question,
We know that the external angle is equal to the sum of opposite two internal angles.
Therefore from the figure we have,
………………….(1)
…………………(2)
…………………..(3)
Adding the equation (1), (2) and (3) , then we get
We know that the sum of all the angles about a point is equal to .
Therefore, by the point we can get
Hence,
Therefore, Lines , and intersect at a common point as shown in figure. is joined to , to and to to form a triangle.
The value of is is
Hence option is the correct answer.
So, the correct answer is “Option B”.
Note: Triangle is a closed figure bounded by a three line segment.
There are three types of triangle : scalene triangle, equilateral triangle and isosceles triangle.
Sum of all the angle of a triangle is
External angle is equal to sum of opposite two internal angles.
Sum of all the angles about a point is equal to .
We will use the fact that the external angle of a triangle is equal to the sum of opposite two internal angles. For example: in the above figure
i.e.
Complete step by step solution:
This problem is based on triangles. Triangle is a closed figure bounded by a three line segment. A triangle has three vertices, three sides and three angles.
The given diagram is mentioned below,

Let us assume, the Sum of all the angles in a triangle is
Consider the given question,
We know that the external angle is equal to the sum of opposite two internal angles.
Therefore from the figure we have,
Adding the equation (1), (2) and (3) , then we get
We know that the sum of all the angles about a point is equal to
Therefore, by the point
Hence,
Therefore, Lines
The value of is
Hence option
So, the correct answer is “Option B”.
Note: Triangle is a closed figure bounded by a three line segment.
There are three types of triangle : scalene triangle, equilateral triangle and isosceles triangle.
Sum of all the angle of a triangle is
External angle is equal to sum of opposite two internal angles.
Sum of all the angles about a point is equal to
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