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Answer:

[tex]{\angle}ABC=41^{\circ}[/tex]

Step-by-step explanation:

From, the given figure, it is given that [tex]{\angle}BAC=72^{\circ}[/tex] and  [tex]{\angle}BCD=113^{\circ}[/tex].

Using the exterior angle property in ΔABC, we have

[tex]{\angle}ABC+{\angle}BAC={\angle}BCD[/tex]

⇒[tex]{\angle}ABC+72^{\circ}=113^{\circ}[/tex]

⇒[tex]{\angle}ABC=113^{\circ}-72^{\circ}[/tex]

⇒[tex]{\angle}ABC=41^{\circ}[/tex]

Therefore, the measure of [tex]{\angle}B[/tex] is [tex]41^{\circ}[/tex].

The list of the steps should be explained below:

  • The calculation is as follows:

Triangle has 3 angles, A, B, C.

The total interior angle of a triangle is 180.

Now

180 = A + B + C

180 = 72 + B + 113

180 = B + 185

B = 180 - 185

B = -5

So, the above proves that the figure is not a triangle because angle B is negative

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