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Q.

Find the value of x in the following triangle.


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a

124°

b

134°

c

144°

d

154° 

answer is A.

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Detailed Solution

Concept: 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∠BCA that is value of x by the interior angle sum property of triangle.
Now, from figure we can see that in
triangle △ABC, ∠ABC=24°, ∠CAB=32° and ∠BCA=x°
Also, ∠ABC≠∠CAB so triangle △ABC is a scalene triangle because ∠ABC≠∠CAB which conclude sides BC≠CA≠AB.
Interior angle property states that sum of angles in a triangle is 180°.
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° Assume this as equation (1)
Substituting values of which are given in figures,
as ∠ABC=24°, ∠CAB=32°and ∠BCA=x° in equation (1) , 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°=180°-56°,
Subtracting 56° from 180°, we get
x°=124° Hence, the correct option is 1.
 
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Find the value of x in the following triangle.