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. (Please list just the numerical values with a space in between. No comamas. No variables)
Answers
GPT 3.5
The sum of the three angles in a triangle is always 180 degrees.
Therefore, we can set up the following equation:
(8c + 10) + (3c - 20) + (5c + 30) = 180
Simplifying this equation, we get:
16c + 20 = 180
Subtracting 20 from both sides:
16c = 160
Dividing both sides by 16:
c = 10
Replacing c in the original equation with its value:
(8c + 10) + (3c - 20) + (5c + 30) = 180
(8(10) + 10) + (3(10) - 20) + (5(10) + 30) = 180
(80 + 10) + (30-20) + (50 + 30) = 180
90 + 10 + 80 = 180
180 = 180
Therefore, the value of c is 10 and the measures of the three angles are 90 degrees, 20 degrees, and 80 degrees.
Answer: 90 20 80
Therefore, we can set up the following equation:
(8c + 10) + (3c - 20) + (5c + 30) = 180
Simplifying this equation, we get:
16c + 20 = 180
Subtracting 20 from both sides:
16c = 160
Dividing both sides by 16:
c = 10
Replacing c in the original equation with its value:
(8c + 10) + (3c - 20) + (5c + 30) = 180
(8(10) + 10) + (3(10) - 20) + (5(10) + 30) = 180
(80 + 10) + (30-20) + (50 + 30) = 180
90 + 10 + 80 = 180
180 = 180
Therefore, the value of c is 10 and the measures of the three angles are 90 degrees, 20 degrees, and 80 degrees.
Answer: 90 20 80