Interior angles

Calculate the interior angles of a triangle that are in the ratio 2: 3: 4.

Correct answer:

A =  40 °
B =  60 °
C =  80 °

Step-by-step explanation:

$$\begin{gathered} A+B+C=180\mathrm{°} \\ A:B:C=2:3:4 \\ A=2d \\ B=3d \\ C=4d \\ 2d+3d+4d=180\mathrm{°} \\ d={\displaystyle \frac{180}{2+3+4}}=20\text{ ° } \\ A=2\cdot d=2\cdot 20=40\text{°} \end{gathered}$$

$B=3\cdot d=3\cdot 20=60\text{°}$

$$\begin{gathered} C=4\cdot d=4\cdot 20=80=80\text{° } \\ \text{ Verifying Solution: } \\ s=A+B+C=40+60+80=180\text{ °} \end{gathered}$$

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