in $ \triangle abc, ab = 4, bc = 7 $, and $ ac = 10 $. which statement is true?
1 $ m\angle bm\angle cm\angle a $
2 $ m\angle bm\angle am\angle c $
3 $ m\angle cm\angle bm\angle a $
4 $ m\angle cm\angle am\angle b $

Question

in $ \triangle abc, ab = 4, bc = 7 $, and $ ac = 10 $. which statement is true?
1 $ m\angle b>m\angle c>m\angle a $
2 $ m\angle b>m\angle a>m\angle c $
3 $ m\angle c>m\angle b>m\angle a $
4 $ m\angle c>m\angle a>m\angle b $

Accepted Answer

# Explanation:
## Step1: Recall the triangle side - angle relationship
In a triangle, the larger side is opposite the larger angle.
## Step2: Identify the sides and their opposite angles
In $\triangle ABC$, side $AB = 4$ is opposite $\angle C$, side $BC=7$ is opposite $\angle A$, and side $AC = 10$ is opposite $\angle B$.
## Step3: Compare the side lengths
Since $AC>BC>AB$ (i.e., $10 > 7>4$).
## Step4: Compare the angles using the side - angle relationship
The angle opposite $AC$ ($\angle B$), the angle opposite $BC$ ($\angle A$), and the angle opposite $AB$ ($\angle C$). So $m\angle B>m\angle A>m\angle C$

# Answer:
2. $m\angle B>m\angle A>m\angle C$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the triangle side - angle relationship

Step2: Identify the sides and their opposite angles

Step3: Compare the side lengths

Step4: Compare the angles using the side - angle relationship

Answer: