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In ABC the measure of the largest angle 32 less than 3 time the smallest angle the measure of the middle angle is 8 more than half the measure of the largest angle . What is the measure of the middle angle?

Respuesta :

JeanaShupp

Answer: The measure of the middle angle = 52°

Step-by-step explanation:

Let x = Smallest angle.

largest angle = [tex]3x-32[/tex]

Middle angle= [tex]8+\dfrac12 (3x-32)[/tex]

Sum of all angles in a triangle is 180 degrees.

So, Smallest angle+ largest angle+ Middle angle = 180°

[tex]\Rightarrow\ x+8+\dfrac12 (3x-32)+3x-32=180\\\\\Rightarrow\ 4x-24+\dfrac{3x}{2}-16=180\\\\\Rightarrow\ \dfrac{2\times4x+3x}{2}-40=180\\\\\Rightarrow\ \dfrac{11x}{2}-40=180\\\\\Rightarrow\ \dfrac{11x}{2}=220\\\\\Rightarrow\ x=\dfrac{220\times2}{11}\\\\\Rightarrow\ x= 40[/tex]

Now , Middle angle= [tex]8+\dfrac12 (3(40)-32)=8+\dfrac12 (120-32)[/tex]

[tex]=8+\dfrac12 (88)\\\\=8+44\\\\=52[/tex]

Hence, the measure of the middle angle = 52°