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

1 answer

To find the value of c, we can set up an equation involving the sum of the angles of a triangle:

8c + 10 + 3c - 20 + 5c + 30 = 180

Combining like terms, we get:

16c + 20 = 180

Subtracting 20 from both sides:

16c = 160

Dividing both sides by 16:

c = 10

Therefore, c = 10.

Substituting c = 10 into the expressions for the three angles, we can find their measures:

Angle 1: 8c + 10 = 8(10) + 10 = 80 + 10 = 90 degrees

Angle 2: 3c - 20 = 3(10) - 20 = 30 - 20 = 10 degrees

Angle 3: 5c + 30 = 5(10) + 30 = 50 + 30 = 80 degrees

Therefore, the measures of the three angles are:

Angle 1: 90 degrees

Angle 2: 10 degrees

Angle 3: 80 degrees