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Find the value of x in the following triangle.

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124 °

134 °

144 °

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 \neq ∠ CAB

so triangle

△ ABC

is a scalene triangle because

∠ ABC \neq ∠ CAB

which conclude sides

BC \neq CA \neq 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 \circ + 24 \circ + x \circ = 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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