Answer:
c is 30.
The angles, from left to right, are:
66, 94, and 20.
Step-by-step explanation:
The three angles form a straight angle. In other words, they sum to 180. So, we can write the following equation:
[tex](2c+6)+(3c+4)+(\frac{1}{2}c+5)=180[/tex]
Let's solve for c. Combine like terms:
[tex](2c+3c+0.5c)+(6+4+5)=180[/tex]
Add:
[tex]5.5c+15=180[/tex]
Subtract 15 from both sides:
[tex]5.5c=165[/tex]
Divide both sides by 5.5:
[tex]c=30[/tex]
So, the value of c is 30.
Now, substitute it into each of the angles to find their respective measures.
Left-Most Angle:
We have:
[tex]2c+6[/tex]
Substitute 30 for c. This yields:
[tex]=2(30)+6[/tex]
Multiply and add:
[tex]=60+6=66[/tex]
Middle Angle:
We have:
[tex]3c+4[/tex]
Substitute 30 for c:
[tex]=3(30)+4[/tex]
Multiply and add:
[tex]=90+4=94[/tex]
Right-Most Angle:
We have:
[tex]\frac{1}{2}c+5[/tex]
Substitute 30 for c:
[tex]=\frac{1}{2}(30)+5[/tex]
Multiply and add:
[tex]=15+5=20[/tex]
So, our angles, from left to right, are: 66, 94, and 20.
And the value of c is 30.
And we're done!
