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The measure of one angle in a triangle is 8c + 10 degrees, the second angle is 3c - 20 degrees, and the third angle is 5c + 30 degrees. Find the value of c and the measures of all three angles.
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The sum of the measures of the three angles in a triangle is always 180 degrees. So, I can set up the equation:
(8c + 10) + (3c - 20) + (5c + 30) = 180
Simplifying the equation, I get:
8c + 10 + 3c - 20 + 5c + 30 = 180
Combining like terms, I have:
16c + 20 = 180
Subtracting 20 from both sides gives:
16c = 160
Dividing both sides by 16, I find:
c = 10
Now that I know the value of c, I can substitute it back into the expressions for each angle.
For the first angle, I have:
8c + 10 = 8(10) + 10 = 80 + 10 = 90 degrees
For the second angle, I have:
3c - 20 = 3(10) - 20 = 30 - 20 = 10 degrees
For the third angle, I have:
5c + 30 = 5(10) + 30 = 50 + 30 = 80 degrees
So, the value of c is 10, and the measures of the three angles are 90 degrees, 10 degrees, and 80 degrees.
shorter
To find the value of c, I set up the equation:
(8c + 10) + (3c - 20) + (5c + 30) = 180
Simplifying, I get:
16c + 20 = 180
Subtracting 20 from both sides:
16c = 160
Dividing by 16, I find:
c = 10
Substituting c back into the expressions for each angle:
First angle: 8c + 10 = 80 + 10 = 90 degrees
Second angle: 3c - 20 = 30 - 20 = 10 degrees
Third angle: 5c + 30 = 50 + 30 = 80 degrees
Therefore, the value of c is 10, and the measures of the three angles are 90 degrees, 10 degrees, and 80 degrees.