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Find the value of x in the following triangle.
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Answer
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Hint: In question it is given that we have a triangle named ABC with angle measure ABC=24 , CAB=32 and BCA=x and we have to calculate measure of BCA that is value of x which we can do easily with property of triangle known as interior sum of triangle is equals to 180 .

Complete step-by-step answer:
ow, from figure we can see that in triangle ABC , ABC=24 , CAB=32 and BCA=x
Also , ABCCAB so triangle ABC is a scalene triangle because ABCCAB which conclude sides BCCAAB.
There is a triangle property of triangles which is known as interior angle sum property. interior angle sum property states that if we have a triangle say ABC, does not matter it is equilateral triangle, isosceles triangle or scalene triangle, the sum of all three interior angles namely ABC , CAB and BCA is always equals to 180 that is ABC+CAB+BCA=180
Now, for the figure given in question we have a triangle named ABC with angle measure ABC=24 , CAB=32 and BCA=x and we have to calculate measure of BCA that is value of x .
So, using the property of interior angle sum property in triangle ABC , we get
ABC+CAB+BCA=180……. ( i )
Substituting values of which are given in figure as ABC=24 , CAB=32 and BCA=x in equation ( i ), we get
32+24+x=180 ,
On simplifying , we get
56+x=180 ,
Shifting 56 from left hand side to right hand side , we get
x=18056
Subtracting 56 from 180 , we get
x=124
So, the measure of angle BCA=x is equals to x=124 by interior angle sum property .


Note: While solving the numerical based on angles of triangle, or any other polygon, one must know the sum of interior angles or that polygon. In the calculation part, we should be careful that there must not be any calculation error as it may change the answer .


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