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Question

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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2 points

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Answer 1

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.

Answer 2

shorter

Answer 3

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.